My son’s college in NY has required students to get a flu shot for the last two academic years. Not sure if it was required before that. In fact, I just did a quick google search and found several links indicating that since Covid hit, more than a few universities besides my son’s college, including the entire UC system, JHU and Elon, have started requiring flu vaccines.
Sorry to veer away from the OP’s question, but wanted to point out while you might not know any, there are definitely schools who have mandated the flu vaccine.