I think what people see as wrong with it is these sorts of gestures are usually actually shaving your hair off in support. As a way of saying you're in this together and there to support the individual. This method comes off as disingenuous because you can just take the cap off and go back to your normal life, the other person can't.

Ultimately it's between them, but if you're going to publicize it. It comes off as shallow and an attempt at making yourself a part of someone else's illness