I don’t know if it’s quite that inveterate. For example, I think you could say that a key presupposition of technocratic governance is that engineers should be made part of the sovereign ruling class.
But look, I’m not knocking the hypothesis. But it is the sort of thing that can be difficult to falsify.
For example, in a book about the American Revolution, Gordon Wood describes pre-revolutionary American society. He describes the hierarchical relations that existed between various classes, and also the distinction between patricians (or gentlemen) and plebeians. It’s really, really fascinating how similar the society he describes is to Plato’s Republic. In light of Wood’s work, Alexander Hamilton’s fixation with honor doesn’t seem like a personal idiosyncrasy, as much as a sign that he belonged to a social class that effectively reproduced many of the norms of Plato’s guardian class (and of course you can see how the mores and norms of that class were preserved by the feudal age — or at least you can imagine it).
But the thing is also that Plato is influencing how Wood is telling the historical story, even if only indirectly. If you look at his footnotes, you’ll see that he often cites Hannah Arendt’s Human Condition, which draws heavily from Plato and Aristotle and preserves a lot of their distinctions. In other words, they’re an indirect influence on Wood that shapes how he built up his story about pre-Revolutionary American society.
So I’m not sure that many of these ideas are quite as sticky as you claim. It could be that among academics certain texts are difficult influences to shake off once they’ve been read, but that those ideas have less of a grip on people who aren’t as familiar with them. After all, there are all sorts of other schematic reasons why a person imaging a society from the ground up would, for example, not think of military folk as laborers. It could be, for example, that they see military labor as a public service, thus making it have more in common with political rule than other forms of physical labor.