I have yet to see an "abolish standardized tests" type suggest a workable alternative (or even an unworkable one).
1.) You're throwing out a signal that has proven to be pretty reliable in at least establishing a floor as what students have a good chance of succeeding and
2.) As a related matter, it's a very simple, quantitative, standardized metric (with decent predictive power) that lets you bucket applicants pretty easily.
Do you maybe throw out some applicants who are really bad at standardized tests, but would otherwise thrive in an undergraduate academic setting? Probably. But the data suggests that standardized testing is a pretty good predictor of success in school (which, of course, is not necessarily the same as success in life).
This might be great for rich kids, though in case you are ambitious, clever, gritty but come from not-so-privileged background (not necessarily low-class or third world - just temporary economic turmoil is enough) - you are going to hate every single second you spend there with all your heart.
So maybe this way it is a win-win in the end. The aristocracy get their titles and the plebs their opportunities for self-realisation. No harm done.
If you're not including self study, then maybe? But with prep and self study, everyone I knew was able to get at least a 100 point increase, I think I got a 300 point increase. Basically aced the math section through practice and study (missed 1 question).
Now let's compare that to other criteria used in the college admissions process.
It's way easier to have impressive and relevant extracurricular activities if you're rich and go to a good school. And unlike SAT prep, acquiring good extracurriculars will definitely take years of your time and money.
Well-written admissions essay? MIT requires one. But you do it at home, instead of a tightly controlled testing center. So if you're rich enough, you can have ghost-written admissions essays. Needless to say, this process can turn even a completely worthless essay into an impressive one.
Creative portfolio? Unless you're in the 99th percentile of musical talent, the difference between "I write songs that I play on an old guitar" and "an orchestra performed my composition" is money. The former is probably not even 75th percentile; the latter, probably 95+.
Alumni parents who would be likely to donate big bucks? You don't need an expensive prep course to get that, yet it can provide your application with a much bigger boost than 100 SAT points. And unlike the SAT, if you don't have alumni parents to begin with, then you'll never get this boost, no matter how much extra work you put in.
The SAT is not fair. But it's the fairest admissions criterion used by U.S. universities today.
(note: MIT still relies on the SAT; today's announcement concerns the SAT Subject Tests)