I beg to differ. The game doesn’t change that quickly. While in the 80s and early 90s Stanford was generally considered a notch below HYP for undergrad it was still considered right after those three by most people. About 20 or so years ago it achieved a status on par with HYP and in the last 10 years or so it has surpassed Yale and Princeton and is considered one of the 2 top dogs of higher ed along with Harvard.
Even more importantly, the ascent of Stanford in public opinion had a whole lot to do with the rise of tech and silicon valley. My opinion is that for a school to meaningfully ascend to the very top and be considered fully on HYPSM level, something organic and seismic needs to happen. Clever admissions tactics won’t cut it just like they haven’t cut it for many other top schools who have tried over the years to ascend in the USNews rankings in hopes that they will be considered on par with HYPSM. I would argue that at this level, the individual positions of the USNews dont matter that much. Princeton has been ranked #1 forever and still is not seen as more desirable than Harvard or Stanford. A few non-HYPSM schools have managed to achieve and maintain a top 5 spot for quite a few years and still they are not considered on par with HYPSM. Getting into the USNews top 10 is a huge deal but once you are in there are other forces at play that determine the pecking order and they are pretty hard to bend.
Truth of the matter is most (but not all) tippy top students are aiming first for one or more HYPSM schools. Some weigh their options and go for the less risky options of ED at other top schools they really like, but even most of them would gladly choose HYPSM if afforded the option. The sheer prestige of HYPSM is light years ahead of any other top US school and is hard to turn down.
HYPSM do not offer all the same thing. The run the gamut when it comes to class sizes, campus types, undergrad focus, academic philosophies, academic strengths.