The French managed something like this in New France with the
seigneurial system. But the basic problem is scarcity of land. In Europe where you have a fixed amount of useful agricultural land and a comparatively large and growing number of people the power and financial heft of major landowner's kept the aristocracy on top long after the feudal system which had created it died out. It was even strengthened in some ways with the industrial revolution as sub-surface mineral rights to coal and iron provided another major boost to landowners. Add to that the British habit of ennobling people who got seriously rich in other ways e.g. the
Earls of Harewood descended from a spectacularly successful sugar trader/planter and you have the British peerage that right up until the mid 1800's.
The problem why that didn't translate into the new world was that land was cheap and plentiful while people were scarce. That meant agricultural land prices were incredibly low and that in turn meant that
landed estates supporting a noble family on the European model simply didn't work. The idea that you could judge someones wealth and importance based on the acreage they owned and then have that reflected by their peerage title broke down.
In the South you had something similar but different there you had a landed class being supported by slavery, that enabled the existence of a class of ultra-rich agricultural producers who didn't actually have to work but could simply live of the labour of others. While culturally they was modelled themselves on the established aristocratic traditions of Britain economically it was much closer to the Russian system where wealth was measured by the number of "souls" (serfs) a noble owned not his acreage. You could see the same thing in Spanish America as well.
Now ennobling the Southern Plantation Gentry is your best route to having an American aristocracy if you want one.