> wouldn't it be better to have all this power be in the hands of the democratically chosen, versus billionaires
Sure. If you want your money to go to the causes that everybody else supports, then absolutely, you should give more money to the government.
However, if you want the money to go to underfunded fields, or areas in which the government doesn't support at all, then you're left with making contributions to non-governmental charities or organizations.
I regularly donate to the EFF, ACLU, SAF, CBLDF, and St. Jude, Habitat for Humanity, among others. Of that list, only St. Jude and Habitat could be arguably better spent through direct taxation. It's possible that the government does more for children's cancer and housing the homeless than those charities do -- it is not possible that the government does a better job of acting as a watchdog agency for the government than the EFF, ACLU, SAF or CBLDF.
Beyond that, when I donate directly, I get the satisfaction of knowing that none of the money given goes towards causes I do not support, like war-making, privacy violations, etc.