In other words, university presidents and provosts are giving a different answer from what you’re sure is the right one, so they must not know how to follow instructions and/or don’t have the expertise to compare colleges accurately and/or must be looking at various other rankings and thinking about endowments and being affected by their knowledge of all the areas in which UChicago might come up short. Ooookay…
Having demonstrated that H and Y are in fact standouts from the point of view of academic offerings, I’m feeling goalposts moving here, but in any event I don’t know how many students take calculus at UChicago vs. other schools (I think the Core only requires a quarter of math, and it doesn’t have to be calculus), and how much would be covered in three quarters vs. two semesters, and why such an analysis would be anything other than a comparison of math classes. Since your child considered Yale, how do you think a freshman Humanities sequence at UChicago compares to Directed Studies, taken by 10% of Yale first-years? I’m guessing DS is on another level, but either way it proves nothing about comparative academic rigor of the two schools.
On your other points, you haven’t provided any evidence of the purported disconnect between graduate and undergraduate academics at the Ivies other than claiming that Pinker says there’s one at Harvard. Telling @JHS that there must be one anywhere there are strong graduate programs and undergrads who have other interests in addition to academics is wishful thinking - @JHS has told you that that wasn’t the case at Yale when he was there, and I don’t see evidence of it there today. I’m glad you acknowledged that at Yale tenured faculty, even Nobel Prize winners, teach undergrads, even just to dismiss it by saying they aren’t great teachers. I think you’ll find they do so at Harvard, Princeton, etc. as well. If you have enough really bright and committed undergrads, and all these places do, professors are likely to want to work with them.
Again with the “we know this” and “we know that” with no evidence. I’m pretty sure some of your readers here know more Yale faculty than you’ll meet in your lifetime, so here’s a story about one Nobel laureate there who’s been teaching seminars as well as lecture classes for decades and is revered by his students: https://yalealumnimagazine.com/articles/4784-william-nordhaus
That’s just a deflection. My point is that even the people on this thread can’t agree on what the median and mode are or how to measure them; some seem to have a sense that UChicago in general attracts more smart, serious kids who aren’t looking for the atmosphere of an Ivy, so therefore has more of an ”academic culture”, others believe that there are fewer and fewer of those kids at UChicago, which resembles an Ivy more every day, and that HYPSM attract enough super smart kids to ensure that any can find their culture there and will apply, notwithstanding the fact that there’s a lot going on beside pure academics. You’re not going to get any agreement on what the median or the mode are, although I suspect all these places are moving toward one bimodal distribution of Canada Goose coats and hand-me-downs.
Re: the satire, I prefer it. One has to consider the source (the Simpsons has historically had many Harvard grads on its writing staff - see here: https://tv.avclub.com/the-yale-harvard-war-bogs-down-in-an-overstuffed-simpso-1798191070) but there’s evidence of real research, it doesn’t pretend to be more than it is, and it’s pretty funny.