No dog in this hunt, but as my alma mater was mentioned :
I have not studied international recognition of American universities, and have no valid basis to judge this myself.
Increasing undergraduate selectivity is nice, but my guess is international recognition in conventional arts & sciences fields is probably derived mostly from graduate schools, and specifically areas that people get Nobel prizes for. Physical sciences mostly, and economics.
Cornell has traditionally been strong in the physical sciences. though some universities have been yet stronger…
However, conventional Arts & Sciences fields, aside, it is my understanding is that Cornell has traditionally drawn some international recognition for its programs outside of those areas. Particularly in agriculture, engineering, architecture, and, yes, hotel administration. There have been countries whose students go abroad mostly to study agriculture or engineering. A past president of Taiwan received his PhD from Cornell in agriculture. I would guess some people in Taiwan have heard of it, at least.
I do recall reading some survey, someplace, that showed Cornell had better recognition in Asia, and somewhat less in Europe. But I don’t know where that study/survey is now, and I don’t recall how other universities fared (because I don’t care).
My guess is U Penn is primarily known internationally for Wharton. But that one program itself is is really, really famous, I’m guessing. Though maybe some people overseas don’t recognize Wharton is U Penn, that may be a case of over-branding being too successful. But my guess is few universities, if any, have any single program as well known as Wharton. Chicago has a formidable business school too, of course, but my guess it is less famous.
U Chicago is, and has been, one of our great universities. I don’t even get threads that start “meteoric rise”
There are other schools that rose after changing their undergraduate admissions practices, but U Chicago has always been great, well before that. As far as I recall. Its long string of Nobelists and other distinguished faculty probably runs pages. In terms areas of conventional arts & sciences fields, its recognition level should be at or near the very top. But of course it won’t garner international recognition to the extent that such recognition may derive in part from fields that it doesn’t offer.
Also name recognition of universities is almost certainly abetted by association with famous alumni. People who are more likely to get to be famous include politicians, TV personalities, actors, sports people, highest-profile businessmen. A US president is a relatively internationally famous alumnus, for one. Academics are rarely famous.
Also some universities gain, or lose, recognition due to their location. My recollection of that survey I saw was NYU and UCLA were way higher than most US people would put them.
Like I said I have no idea how this actually plays out, I am no expert in international recognition.
But if somebody want to look, there are surveys/ studies of some sort or other.