I know that Plato's Republic isn't supposed to be taken as a concrete, feasible guide on how to create such a society, and that it's more of a discussion of what an ideal society might be and why that is. He glosses over quite a lot of the details of how something could be implemented in practice.
But something bothers me about it. Right at the beginning, when the new republic is established, Plato says that it's necessary to banish everyone over the age of ten (because their minds will have the old society's corruption ingrained into them), and start afresh with those children, whose minds are still receptive to the changes he wants to make.
Here's the problem: How does he intend to support a society consisting only of children? Who will rule that society - him? That's inherently flawed as he himself will be as corrupted by the old society as the people he banished. What about infrastructure? There will need to be farmers, doctors, etc. Children can't do these things as effectively as experienced adults, so there will inevitably need to be assistance from the types of people who were banished, thus corrupting the new society.
How can his republic even get off the ground?