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All true, but there also exist a ton of shitty math teachers who fail to connect with students or give a shit. I struggled all through college and eventually learned it was because of a combination of books and teachers skipping critical steps, and some professors using slightly different math language than I was previously taught, so I thought these were new things but it was just a new termnjnterchangeable with stuff I'd previously done. Especially in various algebra and calculus.
You can't expect some kids to learn and "show their work" if there's actually 10 steps to a problem but you consistently skip 5 of em assuming they just get it. Too many just assume we learned something in prior grades that we actually didnt.
The real issue is that they are teaching arithmetic as though it is just playing with numbers, rather than that it is the alphabet of an entirely different language that is far more precise than any human language ever could be. I don't know how to fix that because it didn't click for me until Calculus, but that is a root issue, and why there are so many bad math teachers. Admittedly it's very dry material, and I don't know how to get kids excited about math, unless you incorporate it into baking lessons. They all love cookies and cake.