No, I really disagree with most of what you've said here.

The truth is, you can't really know who is gonna perform on not in prépa based on high school results only. I know about people who were really great in high school but failed in prépa, and conversely people who weren't that great in high school and overperformed in prépa. That, plus as I've said this selection tends to be very geographically discriminating, so if what you've said is true it would somehow mean most of the best students would come from Paris. Perceived potential and real potential are two very different things.

In the next paragraphs, I'll talk about the MP prépa because that's what I went through, but I believe it's roughly similar in other prépas.

The prépa matters a lot because, the most prestigious prépa will prepare you specifically for X-ENS, the middle-ranked will prepare you for the Mines and Centrale, and the lowest-ranked will prepare you for CCP. If you're in a low-ranked prépa but you want to prepare the ENS, you'll have to prepare for it by yourself. That's a very, very considerable disadvantage. Of course there's a common program, but the range of what is studied is way, way bigger in the most prestigious prépa - for instance in my prépa in maths we had additional exercises which we were required to know ; when I compared in my school with other students who came from lower-ranked prépa, some of them didn't even know about some of those exercises. It was not only important to know for X-ENS, it made a big part of one of the Centrale exam kinda trivial.

I believe there's also to some extent the fact that the teachers at the most prestigious prépa tend to be the best ones (because those prépa will be attractive for the best teachers) but I'm not sure how this selection works so perhaps I'm a bit wrong here.

Also, yes, the rhythm is obviously way faster so if you're not good enough in this kind of environment you're gonna fail in a prestigious prépa, and if you're good enough for CCP but definitely not X-ENS you'll likely perform better in a middle-ranked prépa. But I really think there's a very sizable portion of students who are good enough for Centrale and Mines and could maybe get X-ENS with proper training and a bit of luck but who are held back by the prépa they're in.

No, and engineering school mostly qualify as Grandes Ecoles (think les Mines, les Ponts, Centrale, etc) - though there can be integrated prépas which is quite different.

However, going to a random countryside Prépa and going to Henri IV or Louis le Grand is not the same thing. In the second case, you'll have a significantly higher chance to get a shot at the top schools. You'll still need to work, you won't "coast through" because of your background, you can still fail but your chances of getting in the top school (so X + 4 ENS for maths sup maths spé for example) will be maybe 25-30% instead of 1-2% from a lower-ranked prépa.

And then, you're more likely to know the prépa system and less likely to be intimidated by it if your parent has gone through a prépa, which is enough to explain the rest of the difference.

And again, geographical inquelities matter more than financial inequalities here. I went through one of those prestigious prépa and was the first student to ever go there from my high school. I've known people there who weren't even first in their high school classroom but who still got there because they were from a reputable, bourgeois parisian high school. In our maths sup of 40 students, there were maybe 6-7 students from the same high school (the one associated with the prépa - because most of those prépa, i.e. henri IV, saint-louis, etc, are also high schools), and at least half were from the "petite couronne". Ironically, the prépa often have affordable boarding facilities and are among the least costly studies you can do.

That's kinda true for Grandes Ecoles, as in the selection process is mainly done through the Concours, but to really be able to prepare yourself for those Concours you need to get through a Prépa, and not only the recruitment process of those Prépa can be quite a bit obscure, the most prestigious one are mainly in Paris or Versailles (with one or two in Lyon) so there's a lot of geographical inequalities as well.

When it comes to elitism and "excellence", the Oxford equivalent would likely be the ENS Ulm, at least for the 20th century. Sartre, Derrida, Foucault, de Beauvoir, etc, all come from there.

And a looot of Fields Medallist.