At some point a test stops becoming a general aptitude test and starts becoming a "how good are you at taking this test" situation. You get specific prep courses designed just around that one specific test and strategies optimized for that specific test. You start selecting for "elite" rather than "smart."
A merit lottery also keeps everybody from having to waste shitloads of time studying for this one test.
Any test checks how good are you at taking this test. I've not seen evidence that at some complexity level it stops correlating with success in university, have you?
The lottery sortition above the minimum standard (which can still be set quite high) is the solution to preventing a competitive monoculture that a strict "top N scores admitted" policy would make.
any tests will always be gamed by those with the resources to game them. either ethically (through special tutors and private programs) or unethically (cheating).
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.
Paying tutors is not gaming the system. It is trying to learn effectively. I get that one wants to avoid creating a system where students are forced to spend too much time to learn purely for competition sake with no real practical need, but still.
The core issue is the pyramid shaped system where not being at one of these super places means that you are out of the competition for best work in general.
If you are genuinely smart you will do well enough on qualify for top schools just by studying at school and on your own and relying on your own ability. And even the best and most expensive tutors cannot do that much to improve your scores if you just don't have the aptitude and discipline.
The system now is far more geared towards sending only rich kids to college than any national testing and admissions system would be.
How do kids end up "genuinely smart" or "have discipline"?
If your parents are rich and have are around and can provide excellent schools, nutrition, love and care, pay for extra-curricular activities etc, you are far more likely to end up being "smart" and "have discipline" than someone who grows up in a family where parents are absent, they have to go to an inner city school, they can't afford school trips, instruments, extra-curricular activities, since they have to have a part time job themselves to make ends meet.
My point is, that SO many of the qualities we think that somehow kids got "innately" are actually purely products of luck and circumstance. The ability to "work hard" isn't a gift some are born with and some are born without, it's learned and modeled from our lives, parents, teachers, experiences etc.
If you never have parents that buy you books and encourage you to read, it's doubtful you will end up being "smart"
I've witnessed this first hand via a friend of the family. Their kid didn't have the grades or entrance exam test scores to study what they wanted at university. So the kid got to take a year off after high school and focus entirely on studying for the entrance exams with regular tutoring from various private tutors. And while their test scores absolutely did improve quite a bit by doing this, they didn't improve enough, and they still ended up having to study at a secondary choice anyway.
That argument has nothing to do with whether it is gaming the system. Just like intentionally buying a house on a good school district is not gaming the system.
A merit lottery also keeps everybody from having to waste shitloads of time studying for this one test.