Let me first say i agree but also let me be little bit hopefully constructively critical.

There is something called (backwards) rationalism.

... a defense mechanism in which apparent logical reasons are given to justify behavior that is motivated by unconscious instinctual impulses. ..

Rationalism also uses logic but not in sense as e.g. math of physic does. So logic is not enough in this broad sense.

So I think that basic science is the way to go in the early education stages alongside with teaching of accepting self critique and mistakes. Showing that everyone can be wrong and can become better at the thing by fixing their mistakes.

So in other words philosophy could make sense in high schools to some degree.