Cut his hair of?

Hallo everybody,
my son just turned three years old and he's very focused on hair since he was born. It started with playing and pulling my hair out and later he pulled his own hair out. Sometimes it's a sign own of anger, sometimes tiredness and sometimes there's no reason (at least not remarkable for me). December was a really bad month. It was St.Nicholas' Day, his birthday, Christmas, New Years Eve and he changed the group in kindergarten. This meant a lot of stress for him, even if it was positive. After this month he had his first bald spot for everyone to see. He didn't stop pulling his hair though we tried to distract him from doing it.
At the moment it's getting a bit better, but baby 2 is going to come in summer and I'm afraid that this could be next situation he can't handle without pulling his hair. His pediatrist told us to cut of his hair, to make him find another way to handle stress. Now I'm not sure if I should do this. He loves his hair (me too) and I don't want him to see it as a punishment for a behaviour he can't control. I don't think that this treats the cause, but perhaps I am wrong. Please help me to make my decision.