I agree. A rep from Hopkins said they don't even look at letters of intent because they believe students can abuse them and they may be writing more than one anyway. Most think that's unethical and dishonest, and I've heard some people say there can be residency application consequences (idk, I guess they can blacklist you? Not sure how that works).
I think Mayo would understand if you send a letter on interest for them being in your top 3 though; many of their students do get other amazing interviews, so they know that they aren't always everyone's top choice, but they certainly are for some! There any many reasons why someone would still choose them over better location or (barely) better research ranking schools though, including personal connection, so that is probably why they are trying to ask for letters or updates to let them know where you stand. Of course, that being said, I think it's also okay to not be sure if they're number 1 within your top 3, because in my opinion, financial aid is a big factor. Just send a letter of interest then, not intent, until you are SURE. As far as sending one if they're in your top 5 instead - I might do an update letter instead. I think it's better to be honest - the school can likely see through who has genuine strong reasons for wanting to go there and who doesn't.