I think what's going on is that there are two very different ways of thinking about questions: rights based and outcomes based. You can have an approach of trying to balance rights (you have a right to heat your house, I have a right to clean air) or you can try to find the best outcome (how does the harm of you freezing to death compare to the harm of me breathing pollution). I think this is part of why I didn't understand how people could answer the question in should we treat inexpensive diseases first differently than I would: they were using a rights based approach (everyone has a right to medical treatment) while I was using an outcomes based approach (more people get treatment).

To an outcomes oriented person, the question of the role of government is an empirical one. What is the effect of public education? Welfare? Consumer protection? Financial regulations? An outcomes oriented person might be an anarchist or libertarian because they believe that government generally makes a mess of these things and, especially after you account for taxes, it would be better to have the government not take on these roles. A rights oriented person, by contrast, might be an anarchist or libertarian because they believe that people have a right to do what they want without government interference. To them, whether governments tend to spend money well is irrelevent.

[1] There are probably exceptions, but I can't think of any where the prospective thief has enough information to know that their case is exceptional.