See CalTech for an example of an elite school that has race-blind admissions. As far as I can tell, it hasn't put any pressure on the Ivy's to change. Incidentally, Caltech's latest class is roughly 50% Asian and about 30% white.
As for CalTech's rep, I'm just one person on the East Coast and wasn't a Tech-type student but I forget it exists all the time. If someone asked me to name a West Coast school to compare to MIT, "Stanford" would be all I could think of.
This is not true. See http://finance.caltech.edu/Resources/cds (pick any year), Section C7.