People don't become "independently wealthy" by saying no to money, they do it by grasping at every bit they can. Wealth is positively, not inversely, correlated to greed. We literally just saw what happens when you put an "independently wealthy" in the oval office, he took a 10 million dollar bribe to greenlight an oil pipeline.
Cap political donations per person and ban corporate donations. Money is not, and should not be legally considered, speech.