This doesn't end at kid level maths either, I have seen people get bachelors and masters in maths without understanding much of it intuitively or being able to apply it.
Mostly because they have rote memorised it (and partly because much of the education system is a game to be played e.g. speaking with professors during office hours can give very strong hints to exams).
Right, I've also seen people that couldn't get some higher math items because they haven't learned to recognize some things on sight. Curves are a good example. You should be able to roughly sight identify basic curves. Or distributions based on their shape. With obvious caveats.
I suspect this is a lot like being able to recognize a piece of art to the artist by sight. Strictly, not required. But a lot of great artists can do it.
For real fun, I saw an interview with Magnus Carlsen where someone was quizzing him on famous games. He was able to say the match on the first 2-3 moves a remarkable number of times.
My professor said this was an inevitability that holds people back who don't understand it is. After a certain point, you can't understand it all, because actually understanding it requires understanding the 1000 page proof. After a certain point, in maths, you must rote memorize the tools, add them to your belt, and trust the centuries of work before you, so you can apply them to your problems. It serves no purpose to "understand" them, many cannot be put into an intuitive framework, and attempting to make "understanding" a prerequisite to your progress will mean you will eventually fail out of the program.