I mean, there is no controversy in mathematics about whether 2+2=4, and yet we continue teaching this knowledge in schools.

Yes, and we continue teaching modus ponens and proof by reductio in philosophy classrooms. (Not to mention historical facts about philosophy.) Here we're changing the subject from 'do issues keep getting talked about equally after they're settled?' to 'do useful facts get taught in class?' The philosopher certainly has plenty of simple equations to appeal to. But the mathematician also has foundational controversies, both settled and open.

Pretended ability to make specific conclusions concerning ill-defined but high-status topics. :(

So if I pretend to be able to make specific conclusions about capital in macroeconomics, I'm doing philosophy?