The short answer
Accreditors recognized by the federal government decide which colleges count, and the colleges they review fund them. Federal student aid flows only to schools a recognized accreditor has approved, which makes accreditation the gate to the money.
Follow the money around the circle. The government lends. The colleges collect. The colleges' own associations decide which colleges count. And licensing boards write that approved degree into law.
Nobody in that circle has a reason to open a second door, because every one of them is paid by the first. The better ways of learning aren't outlawed. They just aren't allowed to count.
The Congressional Research Service describes the funding link: accreditors are funded by the schools they judge. That doesn't make any accreditor dishonest. It means the checker is paid by the checked, and the same structure is why the international standard for certifying people, ISO/IEC 17024, treats training and certification under one roof as a threat to impartiality.
You can see the effect at the edges. Take the CPA 150-hour rule. Andrew Sutherland, Matthias Uckert and Felix Vetter found it cut new accountants by about 14 percent and minority entrants by about 26 percent, with no sign of better quality. And licensing has spread. About one in twenty American jobs needed a license in the 1950s. About one in four does now.
Some of this protects the public. Medical training was reshaped by a 1910 report funded by the Carnegie Foundation, and that closed real quack schools. The gate protected patients and it protected incomes. Both are true.
The fix doesn't need anyone to tear the old gate down. Build a second door beside it, based on proof of skill, and let people walk through.
When you read that a school or a program is accredited, ask who accredits it, who pays the accreditor, and whether the accreditor measures what a graduate can do or the hours and resources behind them.
Some licensing protects the public. The 1910 reforms closed real quack schools. The CPA figures describe one profession. This page is about the incentive in the structure, and it makes no claim about any one accreditor's honesty.
The people who decide which credentials count are paid by those credentials.
Separate the one who teaches from the one who tests, pay the examiner the same whether you pass or fail, record everything and allow appeals, let anyone check the result, and make it update every time it runs.
Nobody has to tear the old gate down. Build a second way in beside it, based on proof of skill, and let people walk through.