The application to elite colleges is more than just a straight numbers game. Essays are intended to help admissions get to know the applicant, to learn how they'd function in the college's community. The idea of spending that precious time to talk about why you made a pair of B's as a sophomore? Freakin yikes my dude. "See, I have this history of anxiety and depression and perfectionism, and I desperately need for yo…
I don't think this is necessarily correct; or, at least, your justification seems incomplete.
Of course if someone could choose between all the Ivies, there would be a single school that best suits them and should be chosen. However, there are certain applicant profiles where the acceptance variance is so high that it becomes completely rational to apply to all Ivies (or at least most of them). Anectodally, the cultured between the Ivies is homogenizing anyway and most students who actually attend have also applied to the other Ivies.