I just went through this process and am a STEM person. I had no desire to fill out supplements about “Why do you want to go to _____ University?” (and pay testing fees to College Board and application fees to said universities) that I did not want to attend. I was an educated shopper, not a trophy hunter or too lazy to look beyond USNews rankings or swayed by the league of a university or maybe I was just picky or whatever one wants to call it. I knew I was a very strong applicant but also that this process is a crapshoot. Half of the Ivies – Brown, Columbia, Cornell, and Dartmouth – did not make my final list based on my rubric and I instead added a few universities, such as Johns Hopkins, that were both higher ranked than these lower Ivies (for what USNews rankings are worth anyway) and better fit for me. In the end I applied to 8 schools, including a couple of fall backs that I could see myself at for the next four years.
I will be attending Yale in September.
Bringing this back to the OP’s question, I did not even remotely think about the SATs freshman year. I took some practice tests on my own from the Big Blue SAT College Board book over the summer before my junior year (but you will be taking the revised/new version so a different book to use) and scored well and only took them once.