[EvgeniyZh]

Any system can and will be cheated, that wasn't the point of neither OP's or mine proposals.

Standardized testing is a good predictor. In my country people are admitted based on standardized testing only (country wide subject exams and sat-like test) or results of university-adjacent "preparation courses" and it works fairly well. The affirmative action is realized directly as a bonus points to your scores based on the background, which reduces the effect of ethical gaming.