The societal benefits of maintaining fairness in opportunities to move up the economic ladder (speaking about India here) far outweighs other criteria. While one could argue that access to coaching institutes creates an unfair barrier on its own, in practice coaching institutes often teach good students of lesser means for free (because they can advertise their results and good results attract more students to coaching institutes).

These top colleges (in India) are literally a pathway to economic betterment of extended families as they're very affordable (lower income families essentially pay no fees), reasonably good and pretty much guarantee an upper middle class exit. I think introducing any shade of unfairness into this process even if it reflects underlying unfairness of life will damage soceital cohesion.

Source: studied in these colleges and know personally several classmates of very modest means whose extended families benefited from their success. Also personally know a few people in China who have equivalent stories.