I had no impostor syndrome. Many of my peers didn't either; it's certainly not the case that almost everyone feels it. There seemed to be little correlation between ability and impostor syndrome too, so it's not a question of ability. But I digress.
Decades out, and understanding university admissions in-and-out:
1) At least an order of magnitude more people "belong" at MIT than there's space for. Elitist universities manufacture scarcity.
2) It's a pretty random process if you get in or not. The level of noise in admissions is huge.
3) It's not a meritocracy otherwise. There isn't a single axis of "quality," and if there were, it's not what admissions selects for. A lot of this became public with the Harvard lawsuit, where it turned out close to half of white students at Harvard got in through back doors (alumni, legacy, children of faculty, athletics, etc.). MIT is different, but no better.
4) Where you go matters a lot less than we make it out to. So much of MIT (and other elite schools) is about building out alumni as brand ambassadors. It's like the magic of Disney -- manufactured by PR departments to fool people. MIT builds itself on being hyper-elite, but there's no difference in quality of individuals at MIT, Georgia Tech, or many other good schools.
5) The elite school advantage is mostly in having a brand stamp and a power network when you graduate, not educational. That helps a lot of you're trying to be a CEO, faculty member, or similar, but not so much for the jobs 90% of my MIT-graduating peers are in. The educational outcomes are the same.
Unfortunately, the "best-and-brightest" brand-building leads to things like impostor syndrome. It may help if you know you were manipulated, but it probably won't. It's pretty deeply embedded in most graduates, and even if you know everything in this post internally, most people take decades to internalize it.
Breaking conditioning is hard.