Then why are colleges fighting for the right to discriminate on race alone (I've seen nothing suggesting that they're looking for economic diversity)?

The claim is that a multiracial student body enriches the educational experience, and there's truth to that. But having representatives of many races actually does little. Having a wife of a different race, I think I'm qualified to claim that racial differences make up the smallest of differences between people. Far more important, in real life as well as outlook on the world, are factors such as religion, urban/rural living, size of family, and more.

I don't see schools concerned about the portion of the student population of Buddhists relative to Catholics, or that there are enough kids who grew up on farms. So long as they are pursuing only racial diversity, I think that their claims about the value of diversity are a sham.