"wouldn't it be better to have all this power be in the hands of the democratically chosen"

This assumes the money in question belongs to the state to begin with, and we're merely deciding how it is to be allocated. That is not the case. This is not the rich deciding what to do with the public money, it's the rich deciding what to do with their own money.

I think we would all agree, regardless of level of income, we would rather our own money be allocated to the causes that we support, rather than the causes that 51% of people support.