That's been a popular view among progressive education reformers as well. It's the basis of Montessori schools, for example. I went to one up through Kindergarten and liked it, finding regular 1st grade utterly dull in comparison. But I don't have a good guess as to whether it would've been a better overall schooling (I still found plenty of time to learn things on my own).
However in parallel to these kinds of views being popular among education reformers, it's also been popular to mock them as idealistic hippie views of education. And a different category of education reformer has had almost 180º opposite ideas, based around standardized, repeatable, scientifically measurable education (the basis of NCLB, MOOCs, etc.).
While a radical departure from the old school methods, Montessori is not intrinsically "progressive". It is built on the idea that there is a clear curriculum with the very big difference being children are primarily responsible for choosing from that menu of options, trusted that their own interests are an adequate guide.
Someone who definitely falls outside the progressive reformers would be John Holt, yet he passionately argues along similar lines as what Kubrick is saying here.
Holt: "... the human animal is a learning animal; we like to learn; we are good at it; we don't need to be shown how or made to do it. What kills the processes are the people interfering with it or trying to regulate it or control it."
By modern definitions, Holt is not even exactly "homeschooling". More accurately, he advocates what would be called "Unschooling" -- the idea that home life observing adults is a more than powerful enough motivator for young children to acquire basic skills.
I've also long liked this Seymour Papert quote vaguely along those lines: http://www.kmjn.org/snippets/papert85_logovisions.html
However in parallel to these kinds of views being popular among education reformers, it's also been popular to mock them as idealistic hippie views of education. And a different category of education reformer has had almost 180º opposite ideas, based around standardized, repeatable, scientifically measurable education (the basis of NCLB, MOOCs, etc.).