Do people actually name-drop university programs/classes/professors in their supplemental essays?

I’m not sure what quaker origins of MIT you’re referring to - I found a list of universities with Quaker origins bu MIT isn’t on it: https://www.quakersintheworld.org/quakers-in-action/71/US-Universities-With-Quaker-Origins

None of the other things you mentioned are specific to MIT, which I always thought was the hallmark of a poorly written “why X” essay. It could just as well apply to Princeton or Cornell or UChicago, I think.