I learned more math in shop class than I did in math class. Trig actually makes sense when you're trying to cut angles right to create a piece of furniture, or figure out how to pattern your rafters to get the right pitch on a roof.
Bringing Python or R in to graph the meaningless functions that we graphed on our TI-83s doesn't add much value - what you are doing is still pointless. If you want to teach high-school-level pre-calculus, I think the best bet would be to offer a 3D graphics course. Jamming math into people's heads without showing them why it would ever be useful is about as effective as jamming a camel through the eye of a needle. You've got to trick people into learning math.
I still think back to diagramms explaining the sinus function on the unit circle and jus have to think how much easier that would have been for the teacher to display in an animation. If that animation was a program written ahead of time that would allow for a lot more interactive exploration. Well, depends, really, watching the teacher plug in numbers is probably even more boring than the drawing, and there is something interesting about reduction of the animation to less dimensions (2D without time), should spur the imagination.
> You've got to trick people into learning math
That's the one I'm opposed to because everyone has different preferences, so this tricking is incompatible with the one to many approach in industrialized education.
On the other hand, I completely agree that the lack of application is often a drag and game-programming was my favorite application, but I did that on my own time and it wouldn't have been fun if I was mandated to do so.
Also, purity in maths is motivated by the variability of applications. Purity is an ideal, of course, but it's one about keeping it simple, which is nice.
As I was saying in the OP, the applications should be individually obvious and hence voluntary. If that could be incorporated into class, that would be great, but the reality looks different. Of course my experience is biased.
If you make programming a math class, people will hate it just the same way they hate math.