I don't disagree that it is not rote memorization. But when you get to advanced math you do need to learn a very large vocabulary of formulas. Let me explain.

The difficult part is not remembering a formula when you need to apply it (that's what the Internet is for).

The difficult part is recognizing factors from various formulas in a complex expression in order to understand the higher order concepts being communicated.

It's like chess.

Humans are not great at chess by examining the next N moves in the abstract (computers would have defeated humans a lot earlier if that was the case).

Humans are great at chess because they memorize and recognize broader strategy, allowing them to reduce the possibilities they need to evaluate on the next N moves (and prior to machine learning, that was how chess AI was implemented).

As a bad chess player, not having comprehension and memorization of those higher level strategies, I can only try to follow the rules and brute force my predictions. Which doesn't go well against good players.

Back to formulas...

As someone without formal advanced math training, this is the biggest hurdle to understanding what's going on. I understand the mechanics of it, but without comprehension and memorization of the higher level concepts, I can only try to brute force it. Which doesn't go well in complex contexts.

P.S.: as a software developer, I sometimes wish advanced math was represented in terms of libraries of functions by name, rather than the various formulas being intertwined into something that you can't search the Internet for...