In the case of barbershops, it's important that they know how to properly clean the stuff that'll be touching hair, as otherwise there are various nasty infestations that can be transferred from person to person.
The article is saying "too high". While it doesn't go out of its way to acknowledge the sorts of needs you refer to, the specific barber example it gives is:
"In Nevada, according to Politico, barbers need more than two years of training to qualify for a license; that’s a high bar to anyone looking to break into the business."
Again using the word high, and it's hard for me to see needing quite that much training to cover the hygiene issues as well as a minimum of technique and practice.
One could compare different states and see how much regulation is enough. The most regulated states are surely regulated too much--infections from visits to barbershops don't even show up in health statistics as a meaningful risk.
It's important that drivers be reasonably competent too, and so we have a licensing program. But it is cheap and quick. (Where "quick" might mean a long line at the DMV, but not an apprenticeship.)
