You still need some licensing to ensure people understand the basics, like hygiene, since everyone has an interest in making sure hairdressers won't spread lice or accidentally cut their customers with dirty tools.
Most of the money in hairdressing is in the complicated stuff. People do this because they want to make a career of it. Maybe you're imagining some kind of two week training program which outputs someone who does nothing but run a clipper over people's heads all day for $5 each. The economics and incentives for that don't make sense to me. People who want ultra cheap cuts will probably just buy their own clippers anyway.
There aren't people regularly dying or winding up in the ER in states that don't require 10 months of expensive training to cut hair, so there is obviously a more reasonable line to draw.
A lot of the training is hands-on. It's a trade school. You're not spending a entire month studying the theory of scissors, you're spending a lot of that time working on many customers under supervision. Even a simple haircut for a man might take a professional 20 minutes. A more complex cut can take longer. A student can take twice as long as a professional. It all takes time. It's a lot of work. I don't know what you can cut out without reducing quality. The fact that all states have converged on similar requirements supports that.
To check that someone can give a haircut safely you have to check that they can give a haircut at all, which means the haircut needs to be at some minimal level of quality.
If you can't give a haircut then you can't give a safe haircut.
Specific example: most people expect a basic haircut for a man to trim around the ears. If I never trim around the ears then maybe I'm being safe, but you can't say I give a safe haircut because I'm not even giving a haircut as most people expect it. In particular I'm avoiding one of the most dangerous parts. You need to watch me trim around the ears in a minimally correct way to make sure I know how to do it safely.
Most of the money in hairdressing is in the complicated stuff. People do this because they want to make a career of it. Maybe you're imagining some kind of two week training program which outputs someone who does nothing but run a clipper over people's heads all day for $5 each. The economics and incentives for that don't make sense to me. People who want ultra cheap cuts will probably just buy their own clippers anyway.