The thing is, getting into a top level school requires maximizing all of GPA, SATs, and what might be called "extracurricular appeal"; this crowds out a bunch of different pursuits, more so than grinding test-taking ability (which has rapidly decreasing marginal returns) alone would. You might hope that those different pursuits being crowded out would instead feed into increased extracurricular appeal, but in practice there's a very particular subset of things that universities care about when it comes to extracurriculars. Indeed, some of them (like leadership activities in 4H, ROTC, or Future Farmers of America) actually hurt your chances of admission, which seems insane if you're looking for a variety of impressive individuals who can bring diverse perspectives.

If I were dictator of college admissions across the US, I'd use tests and GPA to coarsely bucket individuals (into basically capable of doing the work or not at each institution), and use a lottery to distribute spots where demand outstrips supply.