So maybe it's time for math teachers and students to stop worrying about developing strong math problem solving skills (e.g., via math contests, etc.)?
You misunderstand what mathematicians do. My favorite example is this: Birds can fly, but can they use their intuition to create a theory of flight, and then use that to build a plane ? This book by Bessis paints this really well [1].
[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...