Every strong chess player I know actually has sat down and memorized the lines in their repertoire. It's also true that they understand the "why" behind the mov

Every strong chess player I know actually has sat down and memorized the lines in their repertoire. It's also true that they understand the "why" behind the moves but I don't think the memorization is avoidable at a high level. It's not always possible to find tactical compensation over the board, especially when you're running lines that have been tested by an engine, which many people are! Or for instance see the "woodpecker method", which is basically a technique for rote memorization of tactical patterns used by a lot of strong players. (I quit my PhD in mathematics so I have less claim to expertise, but I regularly get smoked by >2000 fide chess players in my local club and talk to them about chess a lot)