But one can still achieve great political power in the US while remaining relatively poor, by exerting intellectual influence. Think of ML King. I don't know if Condi Rice is wealthy or not; she may fit both categories.
You can have upward mobility and oligarchy at the same time. Roman and Athenian republics are good examples of it.
You must be joking. There is a reason "patrician class" has meaning and Periclean Athens was more rigidly structured than Rome.
Of course it had meaning in part because of constant struggle between patrician and plebeian leaders. And plebeians often got upper hand. But the successful plebeians were usually affluent so it would support your position.
Now, do you think that XX century European model where your income is not so important in getting to the political office (you get state election funds and after victory the salary sufficient to make living) is worse or not better?