I think this question is not answerable because the government lacks the feedback necessary to come to the appropriate decision.
Let's consider a slightly different context where the question may be answerable. Suppose that a mine owner has his miners and technicians and people like that in a mine. If the mine collapses he loses most of his employees and he spent years training them and getting them to work well as a team and that sort of thing. There is a possibility the mine could collapse and if the miners aren't rescued he has to find new employees and go through the whole process again. So he might decide that this would be a disaster and that he should insure against it so that if the mine collapses the insurance company will pay to dig out his men. And maybe it will cost $10 million for each man or whatever.
And let's suppose the insurance company provides the coverage. The insurance company has to pay the bills by getting people to give it money because giving the money is better than not doing so. The customers know their money will be used to pay for accidents and that sort of thing. So there is a clear sense in which the insurance company customers consent to pay for whatever the insurance company decides to cover. And there is a check on the company deciding to cover silly things. If the company agrees to pay a man $1 million if he nicks his pinky, it won't last long.
If the company refuses to pay out to rescue the miners then it may be guilty of fraud and some of its staff may face prosecution or fines or something like that. In addition, an insurance company that doesn't pay out when people think it should may lose customers. Customers want the company to pay out when it should because they want to get the money they are insured for under the circumstances stipulated in their contract.
A government is in a very different position from the insurance company. If your decide you don't like something the government is doing and that you would prefer to pay a different group of people to do the same stuff, or pay nobody for the relevant service, you will not get far. The government will take tax money without asking for your consent and if you try to resist you might be imprisoned or killed. You could vote against a government that does something stupid but your vote is only one among millions. You could argue the government shouldn't do something but you would have to persuade something like a plurality of the population to throw out the current government. At that point you get a new government over which you had about the same amount of control as the old, i.e. - negligible control. Since governments have very little in the way of feedback, it's a mistake to expect them to reach the right answer on sophisticated and subtle moral issues. Should the government save some miners? I don't know, and neither does the government.