I suspect you’re correct insofar as the way math has traditionally been taught is likely the antithesis of how it should be taught. I was an adult before I discovered the beauty and real power of math and I’m still in catch-up mode all these decades later. I picked up one or two tidbits during my childhood (my father, an engineer, explained the concept of quickly arriving at the magnitude of the solution in order to conceptualize the result and also check the “worked through” result to confirm the magnitude corresponded) and with these by age 10 I imagined I’d invented the base 10 log concept. But for the most part math was a mechanical non-conceptual subject throughout school, usually taught by people who had no affinity for it. Teaching myself rudimentary calculus was probably a far better approach than learning it in class because I was able to visualize the equations and play with ideas in my head, rather than simply finding the value of the derivative as quickly as possible or calculating the area under the curve to the requisite number of decimal places.
Yet these conceptualizations were still primitive compared to what I learned later: math is astonishingly beautiful. It can do things words are powerless to achieve. The simple formula 1/n is a trivial example: when n is tiny, 1 approaches the infinitely large while conversely when n is large 1 approaches nothingness. No poem or essay can ever convey the wonder of this symmetric concept of vastness and tininess embedded in so few symbols. Vector transformation over a Riemann manifold, the Dirac equation, all these things and so many more are aesthetically rich as well as being highly functional. We don’t learn to read merely to decode bus timetables and cookbook recipes: we learn poetry and literature. I think we need a similar approach to math, wherein the magnificence of its power is conveyed alongside the techniques and concepts we require in order to play with it.