@inn0v8r - I think Yale would be a fantastic choice for many, many students, including some engineering students. I will give you some answers both from my family’s story and also in general:
For my son - he honestly wouldn’t have thought of applying to Yale or having a chance to get in - except a relative suggested it, because admissions can be very random and it’s a great school at the perfect distance from home with a strong Jewish community. He was bowled over to be invited to “YES-W” and had a fabulous time. In fact, for him, YES-W put Yale on the map and became a real contender. The idea is that they have a smaller engineering program that they are actively growing, including a wonderful Maker Space and lots of funding, attention, undergraduate research, etc. And of course it’s in YALE which is pretty special for a zillion other reasons.
However, the financial aid offer came in with us paying about 25 K per year MORE than Princeton’s did. At that point, it would have had to be a much better choice than P (in which case we might have tried to get them to match, but that’s not guaranteed past the first year). Also, Y’s way of calculating FA, apparently, excludes consideration of K-12 expenses for siblings and includes [primary] home equity.
That said, Y is still in third place for my DS - in spite of not having been on his radar before his visit. I would say that’s a big thing and something that Yale should be pleased with, in terms of the success of YES-W, that they really get kids to put Yale on the map.
For kids in general - if someone didn’t need quite the same kind of Jewish community as my DS wanted, as an engineering student, they might add to the application list places like Stanford, UC Berkeley, UIUC, GaTech, Caltech, UT, RPI, and a bunch of others. None of these schools made it to our list, and we were mindful not to have too small a list, in case most did not come through since there is so much randomness. So Yale had a leg up in that way for us, but for a typical kid, its lower rankings in engineering (even compared to many public universities) might lead to less interest. Our reaches of “HYPM” would be replaced in general, I suspect, by “HPMS” for STEM kids.
Also for kids in general - not everyone is sure they will be an engineer, and some who are sure, change their minds. So if you can get into a place like Yale, that seems pretty awesome because you could go into basically any field and do great there.