Buffett's investment during the time were an example of what the private sector can do (and my opinion, as a shareholder of brk.b, who is otherwise not a finance expert, is that the man wasn't nearly greedy enough when others were fearful, but even berkshire doesn't have unlimited reserves.)
I think the big mistake of '08 was 'bailout with insufficient regulation' - if the government does need to do a bailout, that bailout should come with rules to prevent that sort of thing from happening again, and I think that there wasn't enough of that rule making after the '08 crisis.
I was just making a more general statement about the role of government in response to what I thought you were implying by pointing out the differences between how an investment in a failing company (that then doesn't fail because of your money) is accounted for differently than an investment in another person's health or education, even if the latter may net more.
In general I think the government should mostly stick with things that the private sector can't do well. The private sector is really bad at investing in things like healthcare and education for the poor that make people go from being net consumers to net producers. Government should largely focus on the things that government can do effectively but that the private sector can't do effectively. Usually this means providing services to the indigent and providing regulation (not direct ownership) of markets. But there are obviously exceptions, and I agree that '08 was one of those, it was a market failure that was big enough that the private sector couldn't really handle it, and I think direct interference was a net positive, even if I think the government could have done a much better job of it.