Climbing and falling:
Does the story progress when the DM tells the PC, "you fall and take 5 damage. Roll again?"
If the PC has comrades (usually the case), why not just wait for a rope?
Wasn't the initial fall into the 20-foot pit the real penalty?
When I fail a climbing check, it means I stopped climbing because I can't find a decent handhold, not that I fell.
If goblins were shooting arrows at me while I'm climbing, THEN I might fall.
It might be worthwhile to look at a PC's bonuses. A low-Dex PC with no Athletics might fall, sure. But a proficient one with decent Dex doesn't fall. He just gets stuck.
It just doesn't sit well with me, because it makes the outcome reliant on qualitative things like "your goal" rather than quantitative things like "actual distance involved". It feels cheese-able, by a player who carefully declares their goals in such a way that they further their actual goal by failing at their declared goal, or something like that. And I really don't want to encourage that sort of thinking.
Like trying to fly by throwing yourself at the ground - and failing?
It's a highly-engaged player who not only has a goal in mind, but also has plans for the contingencies. It might be cheesing, but it's better than the player who would rather check her Facebook likes than stay engaged.
Really though, if you have a prescribed outcome for whatever the dice turn up, you're wandering away from the role-playing part of RPG.