We were just at Gettysburg College (test optional), where the admissions officer said test scores are required to be considered for merit scholarships. And that some people will see the school’s average SAT is 1320, so they won’t submit a 1290. Which is a bad idea, partly because of the elimination from merit consideration. But also because if you don’t submit scores the school already knows you don’t have a 1320 (or you’d submit) so you might as well tell them you have a 1290 and not an 1180.
As far as I can see, there aren’t that many test-optional schools where submitting a 1300 (which could also be a 1340 or 1360 after a retake or two) is clearly worse than submitting nothing. If you’re more than 100 points below the average, or definitely below the 25th percentile, maybe you want to just let the school guess, but otherwise it probably won’t have much effect either way.