I think part of the solution if you truly want cheaper education is remove all but core classes from the required curriculum so students aren't laying for bs classes majority of them retain none of. Then allow any student to sit in on any class they have personal interest in and allow generic automatic testing so the student can get a general feel for if they learned well enough (though my opinions on testing are low overall, I know many students still like the benchmark).
Free college would just lower acceptance rates at good state schools and allow more people to complete degrees in community colleges. If anything it will make state school degrees even more valuable; roughly the same number of people will graduate from the same school but the cohort will be academically stronger.
IDK what you were imagining exactly with that last bit, but at my old uni you could test out of basically any class by paying $60 and taking essentially the final in the testing center; if you got >70% iirc you got credit for the course and could advance to the next but no a grade.
If anything it will increase value? Don't buy it. What's your reasoning? Look at the value of college today on avg compared to that of 30 years ago and adjust inflation. People pay much more for what they get now than they did then, because of the saturation.
With the last bit - if you major in chemistry you don't have to take art or anything not chemistry. If you're art you take art. It's a sham that you're required to take all those other classes. They do very little for the vast majority, and if you want the knowledge you can take the classes as you'd like.
School shouldn't be job training only. I majored in a stem field and my favorite classes where the ones where I dove into classical literature, believe it or not. Sure, the degree got me my job, but it also exposed me to the liberal arts in a way that would have been impossible if I tried to study it on my own, because it actively challenged me to step into another field for a minute and reach out to unfamiliar sources to build understanding. There's value in being a well rounded, educated citizen, in my book. The academies of ancient Greece weren't training better farmers or builders, they were training better thinkers and therefore better citizens. That's what modern colleges try to do when they make you take liberal arts classes for an engineering degree. And a chemist who's taken time to learn to read, study, and write well is going to be a better professional chemist than someone who's just done grunt work in the lab and slogged through the chem series, because not only has that better scientist also done that, they've polished their intangibles through liberal arts classes.
Why not remove the fat then? If you cut classes, this won't make institutional parasites disappear, as they'll invent other things to justify their existence. I feel the ballooning overhead surrounding the core mission (here: education and scientific research) needs to be addressed directly.