The real answer imo? Stanford is a luxury, and not even a particularly compelling one at that. Are there amazing professors and cutting edge research at the university? Of course. But is it necessary? In my opinion it would be really hard to make a case for it.
For example, the name on the paper when you graduate has to be one of the more cynical compelling reasons. The connections you'll hopefully make there as a student will be invaluable later in life. Some of the most ambitious people make it to these distinguished institution and those people go on even further after they graduate.
