Such a non-issue, but I love consistency, so why not?
Problem
As of right now, if you have the climbing gear you will always climb with them, this is a “problem” when climbing ladders, as it’d be counterintuitive instead of using your hands, same goes for sliding down a ladder, you wouldn’t slide down the steps if you are using your hands, as you have grip.
Solution
As a solution, your animation should change to the hand-climbing whilst removing the picks[1], removing the sliding mechanic should also be a factor, or potentially reduce it to 10%, whatever works best.
Questions & Answers
Why should this be implemented?
I don’t have to keep repeating myself; why not?
Consistency is an excellent thing in games, some people get impressed by the tiniest details, this isn’t a problem per se, but rather is an inconsistency that’ll leave a player slightly confused if they pay attention to it.
Why shouldn't only the animation or sliding be changed?
Because visuals dictate functionality, you’d expect fire to inflict burning and be hot, you’d not expect to slide down a ladder like you would slide down a rock, it’s a matter of perspective.
Would retain pick animation on other non-ladder surfaces. ↩︎

