Apply the same question to jobs and it's easy to see: why is a lossy [interview] filter better than just [firing] those who can't make it?

This has enormous costs to the institution, the teachers/mentors, and of course to the person failing out.

And that's not even factoring in the social and psychological costs.

Disagree. Hiring and firing is better than a bad interview process. The reason we don't have that is due to regulations and litigiousness (and the laws that facilitate it).

IMO failing to get the opportunity is worse than getting the opportunity and failing at it.