How much do schools that require all SAT scores care about all of them?

Don’t trust CB’s list, (or one of the many erroneous PrepScholar lists). CB says the same for Yale, just as a common example, and they explicitly say

Applicants who opt to include scores may choose to report scores from one exam date or multiple exam dates,

A few other small schools have popped up over the last couple of years, but CMU/Georgetown are the big ones. Always check a school’s website for the correct policy. Contact the school if it’s not specified.