Does SAT really not matter after a certain score?

The answer to the title question is “it depends on the college”.

For example, an applicant to the University of Alabama with a 3.5+ GPA will find that a 1600 SAT gives a larger scholarship than a 1590 SAT ( https://afford.ua.edu/scholarships/out-of-state-freshman/ ). But some other state universities are test-blind (e.g. California public universities), test-does-not-matter once a certain GPA or rank threshold is met (e.g. Arizona State University, most Texas public universities for top 10% rank applicants), or test only matters above a test score threshold (e.g. Arizona State University again, most Texas public universities).