The problem with analogies, is that they seem to work on the surface, but often hide flaws in reasoning. In any profession, there are gradations of ability, scope, and intellect. In the same way that there are DIY plumbers, there are business users who automate tasks, but architects, and engineers are the equivalent of mechanical engineers that build water systems and design controls. Yes, you could not be a doctor or lawyer, but those are guild-like with particular requirements, and those professions have a similar hierarchical structuring of ability, from person tending their own minor injuries to medical assistant to nurse to nurse practitioner to physician's assistant, etc. Even then, the requirements behind licensing are driven by the government taking an interest in guaranteeing minimum levels of competency in proprietors serving the public, so even cutting hair requires training and a license.
I was saying this recently to colleagues at work, that the barrier for entry into programming is very low, and that one cannot be a practicing engineer with at least a degree, several years experience, and some successful projects. In the same way, one might be hard-pressed to work professionally as a developer without a similar pedigree.