Cornell CAS, AEM And Engineering are the only colleges/programs tthere that have analogs at the other ivy league schools, hence are most subject to cross-application. Students apply to a particular college there, not to the university as some composite. A student applying to Penn CAS will be probably applying to Cornell CAS, not some composite of Cornell including majors that are not part of Arts & Sciences. Ditto engineering.
I daresay every STEM person in the Ivy league, and in the field of engineering, is aware that Cornell is strong in STEM. Its reputation is not new. I’ve no idea what “most people think” but UIUC is quite well known in STEM fields too.
You are quite obviously not a STEM person.
Regarding financial aid, they say “If you receive a more favorable need-based aid offer from another Ivy League institution, Stanford, Duke, and/or MIT, we welcome the opportunity to match their offer of financial aid.”
Of course they may not match it. But if they match your financial aid, theirs is as good as yours, isn’t it? Seems worthwhile to try, if someone wants to go there.