It depends. I would argue for licensing in fields where improper training can affect lives, safety, and welfare, e.g. Doctors, Mechanics, Engineers, Pilots, etc. We need some kind of way to verify that an individual who proclaims to be a professional in potentially harmful fields has received proper training and can demonstrate that they can perform their work safely.
I don't know enough about the intricacies of hairdressing, but I could definitely see the case be made for at least some kind of training, given that they regularly handle caustic chemicals (think relaxers), heating devices, and sharp objects (i.e. straight-razors). Maybe a certificate would suffice, but I don't know.
On the other hand I would agree that requiring a florist to be licensed, as the article mentions, is probably going too far and most likely used to stifle competition.