I agree with everything @Choatiemom said. Especially the point about kids changing their minds after revisit day…if I had a dime for every time that’s happened.
Also- Applicants thank the AO/School for their hospitality via a Thank You note which is then placed in their file. A well- written TY note also conveys strong interest in one or two (important) things plus mentions who the applicant enjoyed meeting ( coach, department head or teacher ). A TY note (after an interview) is without question the best way to go if an applicant wants to show enthusiasm (and grace) without going overboard.
So… What else do you need ? What do you think a FC letter (on top of everything else) will accomplish? Look- in my mind you’ve already done all the heavy lifting and demonstrated interest . If you want to tell a school that they’re your one and only- that’s up to you but I believe a strong application has already done that for you.