Here's the thing. Most of calculus's power comes from its use as a mechanical calculational system. Hence the name. Archimedes's proof of the surface area and volume of a sphere is far more insightful and explanatory than the standard calculational proof using integration that any unthinking freshman can crank through with ease. As a rule, calculation proceeds by reducing a big problem into a sequence of small, easily dispatched problems, but human understanding usually works the opposite way. So, it's not that calculus cannot be taught in a way that highlights human understanding, but the greatest strength of calculus is that it produces answers whether you understand what you are doing or not.

Great point ! The "recreational" part can be applied to any subject imho.