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.
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.