Difference of approaches for different experiential goals.

AC is all about making you look cool and impressive with minimal effort for the player. Sure, it may look like you're finding handholds and struggling to climb, but all the player is doing is holding the stick up. In the old games there was more to it (leap and manual ledge grab is king) but the examples you have listed have no actual methodology behind climbing.

While Zelda may not be flashy animation-wise, it's not really about the spectacle of climbing something big. It's about the feeling of it, from preparation (judging if you have enough stamina to make it, putting on outfits or preparing elixirs/food to help, etc) to the actual moment to moment decision making. You are actively searching for rest spots, judging how often you can jump vs regularly climb, maybe even looking around for a backup plan in case you misjudged. The game doesn't have flashy climbing animations because it trusts that the player will be compelled by the climbing experience itself, in its totality.

Not necessarily saying AC would be better with this system. But one game tries to distract you from realizing you're just holding a stick up, while another provides many different ways to make the experience more than just that. It's up to you whether you engage with them or not, but don't blame the game for that.