A goal of professionalization was to restrict entry in the profession, to ensure job security. This happened across the board in a wide variety of fields. Mostly college educated work. Later, labor movements were successful in pushing licensing requirements for trade workers as well.
Your argument reads a little like an after the fact rationalization. Yes, we need good doctors, but that's not the reason why SelfStudy Steve can't practice wart removal or write medical marijuana prescriptions without an MD. Physicians have been very succesful in defending the status quo. One particular sleight of hands is perpetuating the myth that the financial commitment when entering medschool is akin to taking a risk. It is decidedly not because the payoff is virtually guaranteed. I'm not necessarily disagreeing, don't get me wrong, that we need skilled medical practitioners, but the profession is the text-book example of rent-seeking, yet somehow it's unseemly to say this out loud.
Anyways, I don't want to make it seem like doctors don't deserve their pay. That's a different question But I think it is perfectly OK for barbers to pursue job security, and do so through means that have a proven track record.
A small unrelated comment, and I forget where I picked this up, but it tickles my funny bone and just wanted to share.
Paradoxically, the professions that are least likely to be able to guarantee a successful outcome, are paid the most. For example, engineers can reasonably guarantee the bridge will stay upright. Once the work is completed, the client too can easily evaluate by having their donkey walk over it first. A librarian can usually say if she'll find an original primary source within a collection, and the patron can verify with a certain amount of confidence when taking delivery that he's handed the real deal.
However, a lawyer will most likely hem and haw if you ask if he can win your case. If you end up losing, it'll be because of a biased jury, or unfavourable public opinion, perhaps the judge was drunk. Grandma died from that infection? The doctor will say it was old age, or the cancer was really strong, or "god works in mysterious ways". And when you are an insurer, did your actuarian really miscalcute the fire risk in that new township, or do you take him at his word and was it really just all a minuscule coincidence that the place burned down?
The bolder the bluff, the higher the reward. Because you didn't go to law school, how would you know if the lawyer didn't miss this&that amendment to this&that ordinance? You didn't go to med school, so how would you know that the doctor did not wing it that particular night, paying more attention to his fantasy football game than meemaw? And are you confident enough in your high school maths to verify the calculations that yielded that bad actuarial table?
Anybody can recognize a bad from a good haircut though.