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Don't forget Illinois House Speaker Mike Madigan's daughter, Lisa Madigan, currently Illinois Attorney General, and one of the names trotted out as a potential replacement for Obama. She's ridden her father's coattails very well.
It's probably a triple-whammy that leads to the aristocratization you lamented -- (1) most Americans can't afford to participate in the political game, which leaves the field most open to those with the money to participate; (2) once a political "brand name" is established by way of a political family, it gives already well-heeled and well-connected family members considerable advantages over unrecognized names; and (3) without public financing of elections, only the very wealthiest (or boldest/most ambitious/craziest) of Americans can risk running without the advantages of incumbency and/or political connections, because the penalty for defeat is less jarring on the already-wealthy and connected.
Some of the Founders probably would be fine with this situation, thinking that only the "best" sort of Americans (e.g., richest) are fit to govern, since they, in theory, have the most to lose, given how well-entrenched they are.
But I would think that more aristocracy is the last thing this country needs, particularly when the problems our country faces requires new thinking, versus the ossified opinions of the privileged.