You'd think, but as the old saying goes: clogs to clogs in three generations.

(Meaning: the first generation starts off poor, is self made, hands over to the second generation which is less dynamic, which hands over to the third who wreck it and end up poor clog wearers again)

Thing is, education is hard and individual potential also varies a lot. We see this with royalty, where you have literally a country's resources to groom someone into being a high level individual who can deal with most social situations, but having them lead and expand a whole country in another issue altogether.

You'll have some Louis XIV sometimes, and many Louis XVI the rest of the time, with sprinkles of Charles II in the mix to spice it up.