Granted in the broader conceptual idea of mathematics as a whole. But MOST people NEVER will study mathematics as a whole. They NEED to be able to do arithmetic not prove the fundamental theorem of counting. They NEED to be able to some basic algebra and some basic geometry.
The idea that some how you can get every one trained as a proof capable mathematician is just plain silliness. Rather like suggesting that because we know how to drive a car we should all be auto mechanics
Or automotive engineers.
I quite agree. I suffered through the first wave of the New Math, and never did understand why they thought it was necessary to try to teach the principles before the mechanics of arithmetic.
Well, actually I do understand. Nobody ever made a name for himself by simply treading in the footsteps of those who went before him, no matter how good the trail was. So “new methods” have to be invented to make a name for their inventors. Unfortunately, “new” does not always mean “better.”