David Graeber in "Bullshit Jobs":
"Once time was money, it became possible to speak of “spending time,” rather than just “passing” it—also of wasting time, killing time, saving time, losing time, racing against time, and so forth. Puritan, Methodist, and evangelical preachers soon began instructing their flocks about the “husbandry of time,” proposing that the careful budgeting of time was the essence of morality. Factories began employing time clocks; workers came to be expected to punch the clock upon entering and leaving; charity schools designed to teach the poor discipline and punctuality gave way to public school systems where students of all social classes were made to get up and march from room to room each hour at the sound of a bell, an arrangement self-consciously designed to train children for future lives of paid factory labor.25"
"25.:Those who designed modern universal education systems were quite explicit about all this: Thompson himself cites a number of them. I remember reading that someone once surveyed American employers about what it was they actually expected when they specified in a job ad that a worker must have a high school degree: a certain level of literacy? Or numeracy? The vast majority said no, a high school education, they found, did not guarantee such things—they mainly expected the worker would be able to show up on time. Interestingly, the more advanced the level of education, however, the more autonomous the students and the more the old episodic pattern of work tends to reemerge."
Of course it's not just getting up and shuffling from class to class, but also waking up regularly, meeting deadlines, managing time efficiently. All of these things combined with the "basic educational foundation" which is in fact largely preparatory for later education and workplace fundamentals does seem to point against your assertions. And, frankly I think it's all harmful.
Edit:
Should probably also indicate that socialization in a hierarchical setting with various modes of authority being assumed while also dealing with virtual strangers at all points in the day is also not unlike work.