If anyone really favored social equality they would support abolishing the elite universities entirely. Anything short of that still produces an identifiable class of people who attended these institutions, and it’s the existence of that class in the first place rather than its partly hereditary nature that runs counter to social equality.

Harvard-style elite universities, absolutely, and actual leftists do support abolishing them.

CMU-style, or ETH-style or Independent University of Moscow-style elite universities are however probably an efficient use of resources.