What about schools where standardized tests are insufficient?

At Caltech and MIT for example they have way more people with very high SAT score than they have openings for. Most admitted students at both have math scores of 790 or 800, and reading/writing averages around 750.

The SAT is not reproducible enough to say that someone who scored say a 790 is better than someone who scored a 780. If both retook the test they would likely get different scores and would have a good chance of finishing in a different order.

Same for other standardized test.

The result then is that after you filter by standardized tests you still end up with a more people than you can admit that have high tests scores that give you no information about who would do well and who would not.

There are plenty of people who can get those high scores but would not be able to handle the class work at Caltech, and from what I've heard the same applies to MIT. To figure out who can actually handle the work they have to look beyond standardized tests.

The inability for a test to have sensitivity at the top end isn’t some fixed property of the universe. It’s just a property of the SAT. Harder tests are possible. The only thing that matters is that candidates know that it’s not at the whim of some human who has decided that 25% Jews is enough or 33% Asians is enough or whatever and that it’s by a fixed scoring rubric.

And then some large number of high scoring candidates will miss out until we have a sufficient number of universities.

Irrespective of the mechanism, it is incredibly racist to use one’s race as a scoring mechanism perhaps by definition.

I'd argue for what the ETH and the Independent University of Moscow do.

Make them sit some of the university's exams, and if they pass they get in.