Interesting questions. It would also remove eyebrows and eyelashes, which serve to protect eyes from dust and things like that. Armpit and pubic hair serve to reduce friction in those areas and prevent chafing. Nostril hair, assuming it would also be gone, is part of the filtering system of the air we breathe. Considering all those health implications, being fully informed before doing it would be really important.

But if someone still wants to do that to themselves, and is an adult capable of making their own decisions, I say let them!

Whether it's possible or not (the core of your question), I have no idea but the other comments seem to have some theories about that.