I've only maybe used differentiation/integration a few times in my professional career (use it more on personal projects actually). That said, having a solid intuition about first/second order derivatives, rates of change, is incredibly valuable when thinking about the world. I probably use this intuition quite a bit in day to day life without even realizing it. I do wish more probability & statistics was taught earlier on though.
I agree on the intuition. But once the intuition and the fundamentals are there, should teenagers spend months crunching calculus heuristics? It's still the way it's taught in Europe and it's incredibly inefficient.
Ironically, if von Neumann was alive today he would probably encourage kids to use some number crunching software rather than "getting used to it". In that sense civilization may actually have regressed since the von Neumann / Feynman days. Ditching pen and paper for sophisticated computing tools gave us nuclear power and moon landings within 20 years.
