@VC25A2, we think alike. Prestige is important because it opens doors, and not just in a career.
If you want prestige among the general public, go to Harvard, Yale, Princeton, MIT, Duke, Stanford, etc. Say those names and the reaction you get will be (especially outside of the Northeast),“wow, you must be really smart.”
Amherst and Williams and the like are superb schools and, among grad school admissions staff, Wall Street banks, and highly-educated people, are very prestigious, and certainly peer schools to MIT, Duke, etc. However, if you mention them to the general public, or to people in parts of the US far away from those schools, you’ll probably get a blank stare.
I speak from experience:
I went to a LAC that is ranked near the top in US News, but even among the general public in the metropolitan area where it’s located, a lot of people hadn’t heard of it. I have to explain to people now (even other people with graduate degrees) where the school is and what it is. I almost always get a blank stare.
I also went to Harvard. I just say “Harvard” to anyone and everyone knows what it is and gives a reaction, particularly far away from Cambridge. Even when I worked in other countries, I simply said “Harvard” and consistently got the same reaction (“wow…”).
In my view, it makes no sense to go to a school that is unknown if you can go to a school that’s known. You’ll toil away under a lot of stress at either place, and both places will have pricetags.