why go for SAT?

The SAT can actually level the playing field. If you go to a mediocre school you're at a significant disadvantage relative to peers at better private schools, but the SAT is an easy number that I think is reasonably correlated with ability (honestly someone who's good at math and has good reading skills is likely to be pretty good at most other things) that can act as a counterweight.

AP and SAT II are actually less likely to serve this purpose because they depend on subject matter knowledge which depends more on quality of education and even more work.

On the other side, according to the essay typer review writers, for those who don't test well, there is a growing subset of schools that are SAT optional. If you don't think the SATs are a good proxy for who you are, they are now a real option.