It should not hurt you phone unless you allow dirt/debris to get stuck between the case and you phone as it can scuff the anodized finish. I would remove it from the case every once in a while and clean things up.
So there should not be any form of problem with using say a very tight case? (Asking cause I tried the new leather cases for the 6S+ and they fit a lot more comfortably, but this one should go for a few weeks)
Not so. Even the tightest case will allow some debris to get in between. Still a good idea to remove the case occasionally for cleaning. 'A lot more comfortably" mean a little more loose and . . . .