>> What groups, experiences, or attributes does it select for?
Thats the thing -- it becomes a way for admins to select whomever they want, using their own secret/opaque criteria which may well be biased, unfair, unjust.
In New York City, where I grew up, there has been a huge backlash against entrance examinations for high school. The official stance is they are discriminatory because people could prep for the exams, but a quick survey of the schools reveal "too many" poor Asians were getting in. People who could really afford prep schools were going to private schools and boarding schools. Poorer, but intensely driven students wanting to succeed, were prepping for years for the public school exams and "overrun" the schools.
The city chose only three high schools to focus for desegregation (interestingly, the three which most Asians). Original talks were to move to a "leadership based application system" -- as if people really have opportunities to demonstrate "leadership" at age 13 or 14. Leadership here is a euphemism for "being connected" or "wealthy."
To be fully frank, I admit the tests are not fair. A truly fair system would have as many good schools as students wanting to attend them. But we dont have that -- so instead we all compete for a handful of spots that poor students can afford while the truly wealthy buy their way into wherever they want. It isnt a perfect system. The test may not be perfect -- but perhaps then we should try to improve the test, or understand why some students can/cannot do well on the tests -- rather than creating a secret system where a few people get to decide which poor students get good schooling and who gets to remain stuck in the economic prison for another generation.
Disclosure: I studied for years for these exams, went to an application based NYC high school, and went from below poverty line to well into top 1% income in the span of 8yrs. The schools matter, enormously.