You'd better write one.
Some schools care and some don't. If you do write, it guarantees that the
schools caring about your interest will get your signal.
I made the mistake of not writing "thank you" email after interviews as I
thought no one cares. But the fact is that some schools take the follow up
letter as one positive signal of the candidates' interest about the position
----one recruiter, who had a very nice talk with me during the interview,
told me to write a short line letter to him after interview to show the
committee about my strong preference to this position.