Not only is it entirely *not feasible* and *unlikely* (because, again, all schools are structured around the *interests of the state*), but it's also just... ignoring all of the other potential avenues for learning things.
It's still maintaining the workerist society we currently exist within. It's still privileging certain skills over others. It's still atomising them into *individuals* rather than us remembering that we can do things *collectively*.
"Teach it in school" is literally the laziest way of solving a problem, especially when that problem is largely a result of alienation!