Those things, plus a great education, are only one part of going to an Ivy League (and other highly-selective schools).
The other reason people send their kids to Harvard or Stanford is because those schools are the entrance to the elite reaches of our society. Your friends and classmates at those schools are the future top of their various professions and industries. The price tag is the membership fee that gets you into this exclusive club.
Having a degree from one of these institutions opens a lot of doors.
Hmmmm. The "elite reaches". So we have a caste system in this country after all. All those wonderful speeches about the great "melting pot" and of the American "experiment" has come down to what schools you are able to attend. Sounds like old Europe to me. Sucks. Not my idea of what we founded this country to be. We have become a society of "elites" who "rule". F that!!