I think that's true for one specific kind of wealthy person. Specifically those born into it. Its absolutely not true for the self-made. I do have a solution to this.

If you haven't paid your own bills with money you earned (no jobs from family) for the last 10 years, you can't run for office. Literally the mayor of Seattle has never paid her own bills and her husband has never worked either. There is no universe where someone with that life experience makes a good leader.