The idea of political aristocracy is antithetical to the American ideal. Sure, we have our dalliances with bloodlines here and there — the Adamses in the years after the Revolution, though they should get a pass due to their service in the fight against the crowned, cowardly bully George; the Roosevelts, who shouldn’t — but we have done a remarkably good job of keeping the idea of political meritocracy alive. Typically, these bloodlines self destruct (see: Kennedy, Ted — Chappaquiddick) before they can metastasize too fully into our political bloodstream.
Indeed, one could argue that a, if not the, reason we have President Trump is the American disgust for royal houses: The average American found hateful the idea of yet another contest between Bushes and Clintons. The thought was disgusting enough to radicalize voters into nominating as presidential candidate someone with absolutely no business being within 1,000 yards of the White House.