Stylists do more than just cut hair. It's not unskilled labour. Especially when it comes to dying hair you need to understand the chemical reactions involved and the damage they can do to the skin and hair.

There are a lot of people working in the field who just barely know how to cut hair. But the better ones do more than just design work.

EDIT: For context, in my country (Germany) a lot more occupations are regulated than in the US, including hair stylists / barbers (I don't think we have the distinction). While I agree that for some of the jobs the regulations are too harsh and there are too many hurdles to get foreign qualifications and job experience recognized, I think that the existence of these regulations, especially for jobs that involve exposing customers to hazardous materials, is for the better.