Couldn't agree more. But I'd also like to add that working something out in code makes it more real. Trigonometry didn't seem real to me until I tried to make a simple game. Physics might seem boring until you want to make a ball fly through the air like it does in real life. Suddenly those equations and velocity and acceleration MEAN something. You have to figure it out or it won't work. I think teaching programming together with math and especially physics would enhance the experience for all those subjects.
I think that learning how to debug is also valuable because it teaches the lesson that you don't have to be a genius to solve technical problems: most problems can be solved with persistent effort and thought (the effort may involve learning some essential piece of knowledge that you were missing). This applies to many domains outside programming as well. It can change your outlook from a feeling of helplessness to one of competence.