2 formatting fix, last one I promise
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Short Answer: Yes, technically it is possible that this thought experiment can be morally and ethically appropriate to implement, provided that certain key questions are ethically answered (in actions and policies) as part of said implementation. However there is an immense risk of abusive unethical implementations for which there are ample evidential examples throughout history (see below). Having said that, I am personally of the belief that current civilization is incapable of taking the necessary steps to do this ethically due to what I call "nightmare questions" (see below).

Long Answer: In considering this thought experiment one may have to assemble and synthesize a comprehensive answer from many sources that address a number of key questions (some of which are at least partially addressed in other answers here)...

  • Paramount is the question "What is the agenda of the government education of such children?" This certainly would affect many of the questions asked by the OP (such as religious concerns, psychological well being, etc). For some relevant cases you should examine the historically infamous agendas of assimilation by the various "indigenous boarding schools" such as the Indian Residential Schools of the USA and Canada, as well as New Zealand's Maori Native Schools and even Australia's Stolen Generations. User @Willtech's answer quite correctly asks "who's values"? will be used for raising such children and any meaningful answer about the thought experiment must address this issue.

  • If the agenda of such a government-parentage is strictly biological survival (as is implied in the phrasing of the OP's Question, i.e. "Due to low natality [...]") then the morality issue is satisfied since survival is certainly a moral imperative as long as it does not create permanent harm to bystanders the process (i.e. self-defense is considered morally acceptable in most societies). However one must ask: "Why do the children need a government run parentage for upbringing?" Why couldn't such a desperate-to-survive society/government implement a medical program that would radically increase natality and then distribute the offspring to mandatory fosterages through out the population?

  • If on the other hand the objective of this thought experiment is to socially engineer one or more generations then a whole host of questions arises, not the least of which is Who decides? ... Other items include Why is such social engineering considered necessary?, and What will happen to the existing population once the new generation comes into majority? These are the nightmare questions that basically make me believe it is impossible to do this thought experiment ethically.

  • Another key question is What What formform would such a government "parentage" take? would such a government "parentage" take?** My belief is that the only logical approach would be the tribal model wherein a large number of dedicated caregivers would function as a team-parent and equally function as a collective guard against any abuses of the agenda/objectives for the program. I suggest one place the OP might look for case data on this topic is "It takes a village..., and new roads to get there.", as well as a number of related other works (see this Google Scholar search result for the above article title citations.

Short Answer: Yes, technically it is possible that this thought experiment can be morally and ethically appropriate to implement, provided that certain key questions are ethically answered (in actions and policies) as part of said implementation. However there is an immense risk of abusive unethical implementations for which there are ample evidential examples throughout history (see below). Having said that, I am personally of the belief that current civilization is incapable of taking the necessary steps to do this ethically due to what I call "nightmare questions" (see below).

Long Answer: In considering this thought experiment one may have to assemble and synthesize a comprehensive answer from many sources that address a number of key questions (some of which are at least partially addressed in other answers here)...

  • Paramount is the question "What is the agenda of the government education of such children?" This certainly would affect many of the questions asked by the OP (such as religious concerns, psychological well being, etc). For some relevant cases you should examine the historically infamous agendas of assimilation by the various "indigenous boarding schools" such as the Indian Residential Schools of the USA and Canada, as well as New Zealand's Maori Native Schools and even Australia's Stolen Generations. User @Willtech's answer quite correctly asks "who's values"? will be used for raising such children and any meaningful answer about the thought experiment must address this issue.

  • If the agenda of such a government-parentage is strictly biological survival (as is implied in the phrasing of the OP's Question, i.e. "Due to low natality [...]") then the morality issue is satisfied since survival is certainly a moral imperative as long as it does not create permanent harm to bystanders the process (i.e. self-defense is considered morally acceptable in most societies). However one must ask: "Why do the children need a government run parentage for upbringing?" Why couldn't such a desperate-to-survive society/government implement a medical program that would radically increase natality and then distribute the offspring to mandatory fosterages through out the population?

  • If on the other hand the objective of this thought experiment is to socially engineer one or more generations then a whole host of questions arises, not the least of which is Who decides? ... Other items include Why is such social engineering considered necessary?, and What will happen to the existing population once the new generation comes into majority? These are the nightmare questions that basically make me believe it is impossible to do this thought experiment ethically.

  • Another key question is What form would such a government "parentage" take?** My belief is that the only logical approach would be the tribal model wherein a large number of dedicated caregivers would function as a team-parent and equally function as a collective guard against any abuses of the agenda/objectives for the program. I suggest one place the OP might look for case data on this topic is "It takes a village..., and new roads to get there.", as well as a number of related other works (see this Google Scholar search result for the above article title citations.

Short Answer: Yes, technically it is possible that this thought experiment can be morally and ethically appropriate to implement, provided that certain key questions are ethically answered (in actions and policies) as part of said implementation. However there is an immense risk of abusive unethical implementations for which there are ample evidential examples throughout history (see below). Having said that, I am personally of the belief that current civilization is incapable of taking the necessary steps to do this ethically due to what I call "nightmare questions" (see below).

Long Answer: In considering this thought experiment one may have to assemble and synthesize a comprehensive answer from many sources that address a number of key questions (some of which are at least partially addressed in other answers here)...

  • Paramount is the question "What is the agenda of the government education of such children?" This certainly would affect many of the questions asked by the OP (such as religious concerns, psychological well being, etc). For some relevant cases you should examine the historically infamous agendas of assimilation by the various "indigenous boarding schools" such as the Indian Residential Schools of the USA and Canada, as well as New Zealand's Maori Native Schools and even Australia's Stolen Generations. User @Willtech's answer quite correctly asks "who's values"? will be used for raising such children and any meaningful answer about the thought experiment must address this issue.

  • If the agenda of such a government-parentage is strictly biological survival (as is implied in the phrasing of the OP's Question, i.e. "Due to low natality [...]") then the morality issue is satisfied since survival is certainly a moral imperative as long as it does not create permanent harm to bystanders the process (i.e. self-defense is considered morally acceptable in most societies). However one must ask: "Why do the children need a government run parentage for upbringing?" Why couldn't such a desperate-to-survive society/government implement a medical program that would radically increase natality and then distribute the offspring to mandatory fosterages through out the population?

  • If on the other hand the objective of this thought experiment is to socially engineer one or more generations then a whole host of questions arises, not the least of which is Who decides? ... Other items include Why is such social engineering considered necessary?, and What will happen to the existing population once the new generation comes into majority? These are the nightmare questions that basically make me believe it is impossible to do this thought experiment ethically.

  • Another key question is What form would such a government "parentage" take? My belief is that the only logical approach would be the tribal model wherein a large number of dedicated caregivers would function as a team-parent and equally function as a collective guard against any abuses of the agenda/objectives for the program. I suggest one place the OP might look for case data on this topic is "It takes a village..., and new roads to get there.", as well as a number of related other works (see this Google Scholar search result for the above article title citations.

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Short Answer: Yes, technically it is possible that this thought experiment can be morally and ethically appropriate to implement, provided that certain key questions are ethically answered (in actions and policies) as part of said implementation. However there is an immense risk of abusive unethical implementations for which there are ample evidential examples throughout history (see below). Having said that, I am personally of the belief that current civilization is incapable of taking the necessary steps to do this ethically due to what I call "nightmare questions" (see below).

Long Answer: In considering this thought experiment one may have to assemble and synthesize a comprehensive answer from many sources that address a number of key questions (some of which are at least partially addressed in other answers here)...

  • Paramount is the question "What is the agenda of the government education of such children?" This certainly would affect many of the questions asked by the OP (such as religious concerns, psychological well being, etc). For some relevant cases you should examine the historically infamous agendas of assimilation by the various "indigenous boarding schools" such as the Indian Residential Schools of the USA and Canada, as well as New Zealand's Maori Native Schools and even Australia's Stolen Generations. User @Willtech's answer quite correctly asks "who's values"? will be used for raising such children and any meaningful answer about the thought experiment must address this issue.

  • If the agenda of such a government-parentage is strictly biological survival (as is implied in the phrasing of the OP's Question, i.e. "Due to low natality [...]") then the morality issue is satisfied since survival is certainly a moral imperative as long as it does not create permanent harm to bystanders the process (i.e. self-defense is considered morally acceptable in most societies). However one must ask: "Why do the children need a government run parentage for upbringing?" Why couldn't such a desperate-to-survive society/government implement a medical program that would radically increase natality and then distribute the offspring to mandatory fosterages through out the population?

  • If on the other hand the objective of this thought experiment is to socially engineer one or more generations then a whole host of questions arises, not the least of which is Who decides? ... Other items include Why is such social engineering considered necessary?, and What will happen to the existing population once the new generation comes into majority? These are the nightmare questions that basically make me believe it is impossible to do this thought experiment ethically.

  • Another key question is What form would such a government "parentage" take?** My belief is that the only logical approach would be the tribal model wherein a large number of dedicated caregivers would function as a team-parent and equally function as a collective guard against any abuses of the agenda/objectives for the program. I suggest one place the OP might look for case data on this topic is "It takes a village..., and new roads to get there.", as well as a number of related other works (see this Google Scholar search result for the above article title citations.