Because improperly sanitizing barber tools can absolutely spread disease and you're waving sharp objects near somebodies face, including a child who may not sit still.
Do you really need 1,600 hours of training to learn how to sanitise a pair of scissors? Does that training actually make people less likely to stab someone in the head? Are there alternative routes for hairdressers to demonstrate their competence?
To my mind, it seems far more reasonable for these issues to be addressed through routine inspections and the prompt investigation of complaints. Qualifications may provide supporting evidence for the competence of a practitioner, but they are neither necessary nor sufficient.
Maybe a big chunk of it is an apprenticeship? You learn the skills over a few weeks and then spend the rest of the year practicing before you're fully licensed?
Ever try doing a professional hairstyle? It takes several hundred hours just to learn one. It takes several hours alone just to perform one, many times. I used to be a hair model. I had to sit in a chair in front of about 6,000 students at a casino while the designer explained his haircut to them. That was five hours alone, and my hair hadn't been touched. The next four hours were spent actually working on my hair.
However, very few people go to a barber for a shave anymore. It used to be that most people would go to a barber for a shave, and shaving yourself was unusual. Since the advent of the safety razor, cartridge razor, and electric razor, it's the other way around, where it is unusual to go to a barber for a shave. But in many states, training on shaving is a large part of the training for barbers.
In fact, it also used to be the case that barbers were the surgeons as well, though I don't know how much of that time overlapped with the licensing era.
I don't know how much of the remaining licensing process for modern barbers has to do with actual safety concerns, or is just inherited from the times of barbers being surgeons or doing the majority of shaving with straight razors.
That said, these licenses are typically about $10 and can be completed by online website in about an hour. I would expect something similar could work for hair cutting as well, but probably not for all the more exotic things like hair dying.
The restaurants require licensing out the ass, and I know there are ABC (alcohol handling) certifications required for servers, but cooks don't. At least one person (typically a manager) needs to be ServSafe certified, but that's not a requirement for every worker.
Meanwhile, a hairdresser must be licensed before they can step into a salon and do work. My sister and wife both worked in the industry, and I promise you they would both scoff at the idea of a 1 hour form/test for someone cutting hair. There's a ton of hygiene related things that they need to know to prevent disease transmission from cutting and handling hair daily.
You're plenty free to cut your own hair and that of your friends and family without a license. And you can drive your family around with minimal licensing. But there's a threshold you cross where licensing becomes mandatory.
I can drive a car in public and kill other people, not only my own family. Considering how safe cars are today it's even more likely my family will be safe while I kill other people.
Granted, these requirements loosen after a person reaches a certain age. But they still need to demonstrate an ability to drive and knowledge of the rules of the road before being licensed.
A CDL takes a lot training to earn, and you have to demonstrate a clean driving record for the previous 10 years.
Driving is one of the most dangerous things that ordinary people engage in. You're hundreds of times more likely to kill someone driving than doing any other activity, by virtue of the relative deadliness of motor vehicle accidents, and how much driving the ordinary person does.
That you need 1,600 hours of instruction to cut hair in California, far in excess of what any jurisdiction requires to get a license to drive, is the most blatant demonstration of the injustice of occupational licensing.
We should also really encourage people to wash their hands because that's super important, especially in environments like hospitals and daycares.