I would be cautious about schools that do this. Unless its published that SAT score presence didn't affect chances to get in, I would assume its largely a play to get more applicants to reduce acceptance rate, with no scores counting against you heavily.

Anecdata of 1, but in my grad program, standardized test scores were used to sort students best to worst, and then they were evaluated one by one, given an accept/reject rating until all slots were filled. The score didn't affect your chance of being accepted given you were considered at all, but it did determine the chance of being considered.