I never thought about it that way, but it makes a lot of sense. I know almost nothing about modern Greece and yet I have at least passing familiarity with various elements of ancient Greek philosophy or mythology (through a westernized lens of them anyway). It seems like a very colonizer thing to do. Pick out the parts you want to keep, warp them to your ideology, and erase/ignore/exploit the actually existing society.
It reminds me of the psychology of quoting figures from the past more generally. I don't understand the why very well, but I'm sure there is something to the idea that, at least in the white western context, people will tend to take words more seriously if you frame them as something said in the past by a famous figure (hell, sometimes even a fictional character).
Like if I were to say, "The fall of the US will be marked by the rise of a false populism. With popular will so starkly and continuously buried beneath a facade, the anger at being ignored will rise like never before." I'd probably say I'm being dramatic and trying to sound profound when I'm not. But if I went: "The fall of democracy will be marked by the rise of a false populism. With popular will so starkly and continuously buried beneath a facade, the anger at being ignored will rise like never before." - Socrates
There'd probably be people who would be like, wow, so deep. Socrates got it, even back then.
And it brings me back to the idea that the "white" west is fundamentally stuck in the past. Which is ironic because as you point out, it doesn't have a legacy to be proud of in the first place. So it's stuck in the past yet also stuck pining for a civilization that never was, a profundity of understanding it never had, and a capability it only ever got through things like mass racialized slavery. It has little to actually be proud of, so it steals bits and pieces from others and claims them as its own. And it has plenty to be deeply ashamed of, which it washes away at the altar of "humanity is flawed and broken and fundamentally can't be fixed but you can do some penance and then go do more war crimes."