The solution that better countries have is actually pretty similar in spirit to what I proposed. Germany:
1) Provide valid alternatives to credentialing (e.g. a good trade school path), so they've drained off demand for university-style credential.
2) Strictly limit who can go by a test, so you don't have people wasting their time there.
3) Strictly limit how much they can charge, so they don't compete over providing runaway bloat.
Then you're going to have fewer truly educated people than you could have if you didn't give up on them. Other societies with much better education systems than the US show that it is possible to bring more people aboard.
It will take a reform of the education system, but not a reform that caters to the lucky few who love to learn, but rather one that encourages the love of learning in more people.