Universities are naturally xenophillic--both in their desire to understand more about the world and in their desire to influence it. Exploration and openness to new experiences and ideas are also important intellectual values important to develop in students. All of these are enhanced with a diverse student body.

As a more concrete example... $IVY_LEAGUE doesn't gain that much by having its average standard test score go from the 99th to the 99.5th percentile. From the university's perspective, it gains more by admitting students who spread the influence of the university's ideas, enrich and enlarge context in classroom discussions, etc...