My mother lost all her hair (although, after a course of treatment it has since come back - white, now, rather than red, but at least it's there) and a few years ago, out of the blue, I lost maybe 2/3 of mine (although it's now back to being pretty much normal, if not as astonishingly thick as it was when I was younger), and fwiw I think that it's surprising how much of a sense of self is shaped by something as trivial-seeming as one's hair. Going from normal to bald overnight - I think that 'superficial' doesn't do justice to the visceral impact that hair loss has.

It's an interesting idea for a story, imho.