In general, I think that coalitions to deal with large institutions can be powerful. Unions, for example, can be good for negotiating with employers. Coordinating is a useful mechanism for unbalanced situations.
However, I think that cooperating to *not* attend prestigious universities is just as hard as trying to *not* get people to compete.
You run the same trust issues, and it once again becomes an n-player Prisoner’s Dilemma. That is to say, how can you trust other people to *not* apply if they’re all incentivized to betray each other?
As a last note, if it helps disabuse any notions of hypocrisy, I’ll likely be attending a state university and am currently taking an MOOC.