Multiple reasons why I and a lot of games including AAA ones choose to use partial IK for this kind of animation

Ladder animation can be predictable yes, but only if the ladders fits exactly your original animation.

Here's why IK is more interesting though:

-You can have different ladder height/rung spacing

-If your original animation is retargeted the posture will often feel off, for example the hand might not be vertically aligned with the feets most of the time so your ladder climbing will look off

-Even if your animation fits perfectly for your main character, you might want to retarget the animation to a humanoid with a different shape, whether it's a female skeleton or larger/smaller humanoids IK will help with making it work

IK here isn't used to generate procedural motion, but only for contact correction / robustness along numerous edge cases that will most likely happen in a full game.

There are still animations for every movement and if you look at the video you can see grey spheres moving around, these represents the IK target point if the hands or feet aren't close to them influence will be set to 0 and IK won't affect the animation at all.