Well, it doesn't run on taxes either. Successful societies runs on voluntary exchange.
Given how much of the taxes are paid by the ultra wealthy (most of them), how philanthropic they are (very), and how wasteful the government is (impressively), why would you assume that voluntary philanthropy cannot replace involuntary, state-managed welfare?
Everybody just submitting to the hope that billionaires will take pity on them might even work with a sufficiently benevolent overlord, but you get the same problem as so many alternatives to democracy have: If you concentrate all the power in one person, or a small set of people, it's a breeding ground for corruption. Even if your set of people is entirely benevolent, over time as that set of people change it becomes near certain eventually you'll get people who aren't benevolent, and then everyone is fucked.
Democracy, and taxation-based systems of governmental funding, are less efficient than the best possible case elsewhere, but are primarily valuable for massively reducing the risk and dangers of bad actors. Concentrating power among an elite class has historically always been a fantastic way of increasing the risk and dangers of bad actors instead.