>It removes the particularly heinous problem of government officials spending the public's money on things the public doesn't actually want them to spend it on.
That's actually a good thing in my book. Sometimes the right thing is not the easy or popular one. "Let's cut education spending and increase everybody's salaries instead" would probably be very popular but it might not prove very beneficial in the long term. If you dislike the way the government spends money then you elect a different one. If you don't manage to do that then maybe "the public" doesn't disagree so strongly with the way the money is spent.
More generally if you move this to the private sector then the problem is that you effectively weaken democracy. The rich decides what needs funding while the poor, well, they do poor people stuff I suppose.
If you look at modern western societies the rich already have significantly more power than the average citizen (through lobbying, campaign funding etc...). Do you think that's a positive thing? Do you think we should cut the middle man and let them handle everything directly? Instead of complaining that my government doesn't spend money the way I want to I'll get to complain that Mark Zukerberg and Bill Gates don't spend money the way I want to? How is that a better proposition? Can I vote Bill Gates out? Do I have to become a Dropbox shareholder if I want homeless shelters to be funded?
I'll admit that libertarianism in general baffles me. Many of its proponent seems very clever people, many certainly more clever than I am, yet when I discuss with them I feel like I'm talking with somebody from bizarro-earth. "Finance and banking are out of control, let's deregulate it completely!", "Governments are corrupt, let's give the power directly to the ones doing the corrupting!", "It's getting cold, let's get naked!"