... everyone thinks that their alma mater is "one of the great ones."
It's a peculiar kind of bias, that-- and it's not limited to Ivy alums. The fact of the matter seems to be that any college can be a "great" educational experience for almost any student-- given that the student has the proper mindset and approach.
This sounds like the power of a self-fulfilling prophecy? People looking for a positive experience, find a positive experience. There may be a down-side too: People looking to be victims, can unfortunately find that experience as well. There is good and bad in everything. With flexibility, resilience, grit, and a sense of humor, people can find joy and wisdom in their experiences.
Our family rule is that you go where they will give you money to go for undergrad.
So, desire is irrelevant to the question, since it's one of cost.
In light of the psychological inclination to be pleased with one's alma mater, this makes great sense. For many families, this also does not preclude applying to the Ivies.
