[A. Pole]

There are many people in positions of power in the US that have risen from humble means. [...] Power is the reward of the successful

I am not sure what you mean by the success here. Are you saying that people who are poor have a good chance to be in position of power in USA without getting rich first? Or are you saying that even if the most of politicans are affluent still many of them "have risen from humble means" and their position is a just reward?

You can have upward mobility and oligarchy at the same time. Roman and Athenian republics are good examples of it.

[LexBaird]

Both. If one starts from poor and works with dedication and ambition, by the time they become wealthy they have generally learned the skills needed to administer power effectively. Examples include Ronald Reagan and BJ Clinton.

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.