Hair is funny because it can change so radically so quickly. Even though it will grow back out (for most people), there's no hiding it for those weeks or months until it does. You don't get wrinkles, gain weight, get b00bsag, whatever, in 30 minutes without any ability to process the change emotionally, but your hair affects your appearance just as much as those things.

I've definitely had haircuts that have left me in tears, and pretty recently too. Granted a large part of it was tears of frustation with I think six consecutive stylists in my new town who gave me truly horrible haircuts.

Losing a chunk of my breast - even the relatively small chunk of a biopsy - has definitely affected me emotionally. Although of course it's hard to say how much of that is just the appearance (definitely some) and how much seeing it triggers all the emotions that went with it.

I think it's only natural. Look at the displays that animals go through to change their appearance, both voluntary things like puffing out fur, spreading a cobra's hood, etc.; semi-voluntary things like when an animal pumps blood to an area to change its color; and involuntary things like seasonal variations in plumage. Putting on a suit to go to court used to feel like donning a suit of armor (and if you know any mediaeval or classical literature, traditionally there are extended arming scenes where the hero puts on his armor, but also metaphorically and emotionally prepares himself for the conflict).

All anyone has to do is ask yourself whether you'd wear the same clothes to clean toilets and to go to a charity ball, and you have your answer as to how much appearance matters. You can't say that clothes matter but the body underneath doesn't. We don't have to like it, but I think we do have to acknowledge it.