99% of cases, we started out without regulation, but then something bad happens what made us create the regulation.
In china everybody might be able to cut hair, but also anybody is able to drill water wells, and cause massive sinkholes and subsidence all across china. In china you can pollute all you want, and the citizens just have to deal with warnings about toxic air outside on the weather forecast.
Also I'm sure that if you were to ask an actual barber about that licensing they would be able to tell you plenty of good reasons for why that exists. It's not entirely impossible for a barber to screw up somebody's scalp when bleaching their hair for example.