On a college diploma being needed for most jobs in the US:
1. I'll recycle the old joke that most jobs can be performed by anyone with a decent high school education — which is why so many American firms now require an MBA.
2. Back in the 1970s or so, the Sears company — "Sears Roebuck" after Roebuck was purged — required for its management training program "A Bachelors Degree." Never mind from where, never mind in what, never mind your grades or if you had learned anything: A. Bachelor's. Degree. And they had a point. That bachelor's degree requirement was a filter — and a lawful one — cutting down the number of applicants and certifying that for three or four or five years (or more) applicants could mostly stay out of jail, stay out of trouble, follow instructions, and work their way through various complex educational bureaucracies. And applicants would have picked up some skills useful for working at Sears, paid for by the public and not Sears.
Being an effective citizen requires an education. Working as an effective employee mostly involves training, and the immediate question is who will pay for that training. It's highly efficient to have firms training people for the actual jobs they're going to do; it is inefficient to offer generalized training in school. US firms, however, are more than happy to socialize the costs of basic training: their taxes will pretty much remain the same whoever pays to train potential employees.
Back when public schools in the American sense of "public school" were a controversial American idea, Thomas Jefferson thought they'd be good for commerce and all, but that was to boot. The main reason the American Republic (starting back home in Virginia) should have public schools was to preserve the American Republic. Like, if the people are to rule — though who "the people" would be got messy, and bloody — if the people were to rule, the people would need education. On at least one occasion (Notes on Virginia Q.XIV, 1782), Jefferson would have history central to a basic education.