The Ivies seek to maintain their status (derived from wealth and power), which only partially overlaps with what many of us think ought to be their role of educating the very brightest. They have been successful and see little reason to change:
Obama Administration's Private University Background
Inside Higher Education
July 22, 2013
National Journal has just completed its analysis of the college degrees (undergraduate and graduate school) of the top 250 Obama administration officials. The institutions at the top of both lists are private. Of graduate degrees in the senior ranks of the administration, only 25 percent come from public institutions. And while the top five lists lack public U.S. institutions, the University of Oxford does make one of the lists.

Top Universities for 250 Top Obama Administration Officials

Harvard U. -- 23
Yale U. -- 12
Cornell U. -- 11
Princeton U. -- 6
U.S. Military Academy -- 6

Harvard U. -- 38
Georgetown -- 12
U. of Oxford -- 11
Columbia U. -- 9
George Washington U. -- 9

"To see what is in front of one's nose needs a constant struggle." - George Orwell