Because without minimal standards for sterilizing tools, hair dressers can spread lice. Basic licencing requirements give the municipality a chance to ensure that everyone washing hair has been told about basic hygienic standards for washing hair.
Look up Typhoid Mary [0]. We don't licence dish washers because running a restaurant requires adhering to a large body of commercial food safety law that requires the restaurant owner/operator to maintain standards of hygiene. If freelance dish washing were a thing, we probably would licence them.
Having been a microbiologist in a past life I'm very familiar with Typhoid Mary.
I do however think you are attacking a straw man.
"Under Board of Cosmetology regulations, an individual “must complete not less than 300 hours of instruction on the theory and practice of shampooing” at an approved school. That instruction includes how to answer the phone, order products, information about the composition of shampoos, and on the Occupational Safety and Health Administration’s rules governing hair salons."
Would you approve of dishwashers needing 300 hours of training on ordering soap, answering phones, waiting tables, and washing hands?
You ignored the substance of my point: a dishwasher is an employee of a licenced/regulated business operator, who is answerable to a regulatory regime. The state has a regulatory handle on the dishwasher already, and doesn't need to licence them or force them to take training to ensure minimal standards. Cosmetologists are usually independent contractors and are the responsible party, equivalent in legal terms to the restaurant owner/operator, not the dishwasher.
I understand what you are saying. However, I believe your conclusion is absurd. Considering most of the US does not require licensing for a "shampoo technician", it would appear you are arguing for something that is currently a fringe practice to become mainstream. Is that correct?
Also, a cosmetologist and a shampoo technician are two distinct positions.
I'm not arguing for more or less regulation. I'm arguing that we have a societal interest in having some direct or indirect regulatory handle on many jobs that don't obviously require it, and cases like you're raising of the dishwasher, where regulation seems obviously unnecessary, are in fact indirectly regulated--and the costs of regulating the dishwasher, among other restaurant employees, are actually quite significant (meaning that '300 hours' of regulatory training, appropriately targeted at the business owner, isn't as obviously unreasonable as it appears).
You're holding up 300 hours of training for a dishwasher as a reductio ad absurdum of professional regulation of hair washers in salons, when what's obviously happened is a local regulation saying that salon 'workers' (again, actually independent contractors) need a diploma from a cosmetology school. 300 hours is less than 10 weeks of full-time school; a 3 month program teaching salon workers how to effectively, hygienically and with due respect for local business regulations, work in a salon. When you see 'even the hairwasher needs a cosmetology diploma', it's closing a back door where the not-a-cosmetologist hair washer is allowed to do all the things a cosmetologist does for cheaper--and without the required training to actually be an independent contractor.
I'm coming at this from the perspective of someone on my condo building's strata council (i.e. HOA). I'm continually dealing with the push and pull of rules at the most petty level, part of which means people being shockingly petty about avoiding the plain intent of a reasonable rule. You'll never see the truth of the saying 'decisions are made by those who show up' as you will in a minor bureaucratic positions like strata/HOA. It's a constant battle against senior citizens who want your garbage bagged up into one of eight separate classifications and the guy who argues that his truck that hangs six feet out of his stall in the parkade isn't a problem because the rule says "don't block the lane" without specifying by how much.
I'm from a western European nation (often referred to as "socialist") with none of that licensing BS and as far as I know we don't have perpetual lice outbreaks.