To protect consumers effectively, accreditation needs indirect legal protection. Privileged access to public funding is the main weapon. Another is denying the use of certain titles to the unaccredited. I would protect the names university, Ph.D, actuary, and of course accredited, though not college, statistician, philosopher or manicurist. But I’d be hard put to defend these choices in any systematic way.
Apple U., Hamburger U., right out. The jury is out on whether it would be lawful to call oneself a graduate of the school of hard knocks.
And yeah, this is why licensing: because accreditation is ultimately like privately-funded bond rating. And we know how well that worked out.