I disagree with his video. If anything our schools place too much emphasis on future careers, it seems to be the justification for doing everything. The answer to the classic teacher annoyance is of "why are we learning this?" Is always "to get a good job in the future". Slightly better teachers will try to come up with some improbable scenario where the lessons content will prove useful.
The problem with his is that it reduces the value of knowledge to its mere utility. Future careers become extrinsic motivators for learning, thus becoming he entire focus.
There are more reasons to learn something than future usefulness.
What about the inherent value of being informed? We tend to laugh at people that haven't grasped certain basic facts, about history, geography, science etc. by he time they reach adulthood. For example, we would mock someone that couldn't locate a major country on a map, even if hey had no will or reason to visit it."Ignorance is not innocence but sin".
What about learning for appreciation? Bertrand Russell, in his essay "on Useless Knowledge" describes how learning about the history of oranges adds new depths to his experience every time he eats one. You touched on leaning self knowledge, but his can be done in conjunction with learning about other topics, not at the expense of it.
In "On History", Emerson describes how we see ourselves reflected in history, so learning about the great civilisations of he past, we learn about ourselves.
Some knowledge is useful for careers, but the amount of time it would take anyone to master that knowledge required for most jobs is a small fraction of the 15000 hours your average pupil spends in school.
I don't think the problem is in the curriculum so much as the structuring of school. The issue is forcing pupils to study things and requiring that they all follow the same route. Many pupils are put off things that they otherwise would find interesting. If we are lucky, they cram that knowledge before he exams then promptly forget it.
A better school system would be one where here was a far greater ability to follow your interests (though a certain core body of knowledge would remain compulsory), one with far less emphasis on high stakes exams and "learning for working" and finally one which prizes the value of knowledge and learning for its own sake.