Well, the founders of the US thought they'd done a pretty good job of dismantling any aristocracy ... and if you'll recall, one of them advocated for periodic revolutions to keep any such tendencies in check.

More prosaically, the US system, with it's focus on building things up from a low level rather than imposing from above, does offer plenty of prospects to shutter doors to would-be aristocrats ... or would have done, had those local- and state-level organisations stopped playing ball somewhat earlier than this. As it is now, I'm just not sure if the mere fact that the letter of the law is on their side will be enough to counterbalance the immense weight of a US Federal government intent on turning the country it's conquered into a colonial possession.