We have those. They're called "trade schools". The mandated classes are intended to turn out a relatively broadly educated individual. That some people don't take advantage of the opportunity is to their detriment.
Yes, another facet to this problem is the distinction between vocational and liberal arts education. A healthy society needs both, but the higher education has diverted “liberal arts” for different purposes. I’m in favor of completing the necessary liberal arts education during ages 15-20 in one’s home town, before attending other institutions requiring the mandated courses.
Never graduated from college and I can guarantee you that I am better educated across a broader field than 90% of Bachelor's holders out there.