I admit that's a bit of a special case because the AMA restricts accreditation. I would note that schools in the Caribbean have arisen to fill that need - they are notorious for taking students who performed low on the MCAT. I believe the higher debt these students take on is commensurate with physician salaries here are in most cases much higher than in Europe.
Ok so we are talking about colleges that are so bad they don't let you get accreditation for important professions. Not sure if it's what I'm thinking about, but are those the "community colleges", liberal arts universities and stuff like that? In any case you can't study "what you want". You can't become a doctor and I'd guess not an aviation engineer, architect, etc. and expect employment in your field right? Not without going to a "proper" school on debt. That doesn't happen in Europe. There you can get into all those degrees on ~0 cost. For some you need some academic record but I'd argue that's a good thing. A very bad student is never going to finish medicine anyway.
No, medical school is a whole different ballgame. The AMA limits the number of medical students per year and tightly controls the system.
For almost all professions, you can work in that profession after getting a degree from any accredited institution (or often even an unaccredited institution.) Almost all schools are accredited. Virtually every (probably every) public university is accredited and they usually have very low admittance requirements, low costs, and generous scholarships. In many (most?) states, high test scores or a good high school GPA get you a free ride to an in-state public university.
Community college is a good way to get the first two years of a four year degree, or for an Associate's degree that, depending on your field, may be sufficient. They generally also have vocational programs.
You could most certainly become an aviation engineer, architect, etc. by going to almost any school.
The debt story is vastly overblown in the US - it's a serious problem, but mostly among middle-class to upper-middle class families who allow their kids to select the most prestigious and expensive schools, regardless of their academic qualifications, chosen major, or ability to pay. Even in 2017 you can easily get a four-year degree from a good accredited institution and graduate debt free, even if you're not an academic superstar.