This is almost never the case. Power corrupts.
The primary source of political power Jeff Bezos has is his control of a very large employer. Employing lots of people gives you some power over local politics in the areas where you employ those people, and it gives you some level of influence with politicians who might be interested in ensuring you continue to employ lots of people, because it's good for the economy.
Your run of the mill billionaire heir/heiress that doesn't really do any useful economic activity doesn't have a huge amount of political power, in general. They probably have more than you or I do, but not a ton more. Certainly not more in (linear* proportion to the wealth difference.
Once you realize that the relationship between wealth and power is logarithmic, it's not really a super concerning relationship. There are other sources of power that are much more important, and much less transparent.