Visas are issued by the government. All my criticisms still apply, even if the government delegates the decision to the investors.
And no, it works terribly for universities ( or rather, it works great for the universities, terribly for the public). For example, the number of medical schools in the country has actual gone from 162 in 1906, to 129 today, despite a three-fold increase in population. The artificial barrier to entry created by accreditation constricts the supply of medical schools, resulting in higher tuition and higher medical costs.
Or consider law schools. The cheapest law school in Massachusetts costs 38K per year for tuition. If you wanted to create new a law school as a startup, think you could create one just as good for much cheaper? I bet you could. It's not like law schools need expensive equipment. But you're not allowed to, thanks to accreditation laws.
Accreditation started off innocently enough - it was just a good housekeeping seal of approval. But then the professional organizations managed to make it illegal to practice at all without a degree from the accredited institution. The bar associations lobbied for laws that made it impossible to practice law if you simply studied on your own and passed the bar, or if you went through a correspondence course. In 2008, Abe Lincoln is out of luck. Now he has to take on 150K of debt in order to practice law.
History shows the slow is indeed slippery. What if your startup accreditation body follows the path the law schools, and in 30 years ends up lobbying Congress to ban all non-accredited startups?