True, though if socioeconomic status were not correlated with race, then there would be much less of a reason to want to select based on race in the first place.
> There are other non-academic tests like CogAT, Wechsler, etc. that may be even better
They probably would, for a while. Anything different from the SAT/ACT but correlated with some sort of capability is going to do better when the problem is specialized preparation for existing tests. And that was precisely the problem that caused colleges to stop looking at SAT/ACT. It wasn't because the tests are bad. It was the usual "you make what you measure".
Switching tests isn't free, though. You lose all the historical data that show the association between a test and the specific outcome you care about (eg graduation rates at this institution). You have to go through a bootstrapping period, and by the time you're done, it's possible that people are now targeting the new test and it starts losing its utility too.
I think a lot of these types will probably also show up among the people who do extremely well on the SAT and ACT.
There are other non-academic tests like CogAT, Wechsler, etc. that may be even better since they evaluate abstract reasoning and scale from young to old without significant modification. Those are used by gifted programs and organizations like Mensa. It’s possible that these would be adequate replacements for college admissions as well, but you may get a bunch of mildly on-spectrum kids who have never had to work hard for academic success (from my personal experience).