I don't think we're defensive about the intrinsic relevance of math, but, instead, the intrinsic learnability (to coin a phrase) of it. Harvey Becker put it better than I can, but I'd just add, a curriculum composed of interesting problems might very well be more fun, but I don't know where the students will develop the necessary structure of knowledge to solve future problems. I believe we should supply them with the proper structure, then boost them up often to those challenging problems so they have practice doing it.
Basing a curriculum on the specific to the general is like asking Jack Nicklaus to work on his game without ever going to the practice tee. And I wonder how many Super Bowls Joe Montana would've won without ever practicing the basics.