Since there's no such thing as blue blood of course, , and aristocracy only means that at some point in the distant past, a king of some nation, intent on plundering another, rewarded someone's ancestor with a knighthood, or a barony in exchange for being willing to march with him, this is sort of a weird topic. Lots of lesser nobility from England came to the colonies, because England had a system wherein only the oldest male child inherited the title and the land and other male children MIGHT receive some money, if there was any not tied to the rents from the inherited land, (but seldom enough to live extravagantly). Lots of younger brothers of barons, lords and earls joined the military to try to make their fortunes, either the cavalry or as naval men. But again, there was nothing special about these people, because aristocracy is a construct, unrelated to a person's native talent or ability. America, to the Europeans, was a land of farmers and merchants. But having land for the taking (once the natives were dispersed) was a great aid in increasing monetary wealth.
Sad to say, when certain families, over the course of a century or so, built up enough wealth to build mansions and extravagant estates, they felt embarrassed by their merchant backgrounds, and either made up ancestors who didn't exist, or invented some virtue residing in their blood lines to make their success seem aristocratic rather than a product of savvy business skills and luck. They aped the social niceties they observed in Europe, and made their children learn to dance, and to take lessons in speaking French, having nice manners and fine elocution. They were "repaid" when lots of European noble families, whose fortunes were humbled by wars or bad decisions, would "sell" their titles by marrying into these American families in order to get infusions of cash. It is their descendants who still claim this blue blood aristocracy, and they continue to be educated at Eastern boarding schools and at Ivy League colleges as "legacy" admittees.
In a healthy society, there's a constant bubbling, where people of intelligence, energy and talent rise to become leaders and well-respected businessmen, medical people, lawyers, educators, etc. However, over time, wealthy people find ways of gaming the system so that their children will get the better educations, will be first in line for the better jobs, and the tax system will be changed to preserve the wealth of the rich at the expense of everyone else. This is not a healthy thing.