The function of admissions for these institutions is:
1. Secure revenue through donations and full-tuition-paying students to cover their operating costs
2. Boost marketing/PR efforts by maintaining an image of prestige and progressive values.
The prestige of these schools is already unassailable in the public imagination, so this is a simple marketing maneuver in order to maintain a positive image as a progressive institution.
If the goal was to educate as many high-achieving students as possible, they would simply establish testing standards, admit students who pass those standards (pending a holistic review, most likely), hire more world-class professors, and expand the class size.
But increasing the class size of Princeton would also decrease their "exclusiveness" and by extension their prestige.
So in order to balance these concerns, the admissions process needs to walk a tight-rope between admitting desirable minority students that make for good marketing material, "legacy" & wealthy students, and the most academically gifted.
These institutions are structurally positioned to oppose an educational system whose goal is to provide the best education possible to the most students. It's not about equality. In fact, it's about preserving inequality in their favor.