Ridable mobs that can be controlled with WASD and llamas do not receive fall damage while touching vines/ladders

Summary:
Ridable mobs that can be controlled with WASD and llamas are unable to climb on vines/ladders, but do not take damage when falling. Prior to version 1.18, they received fall damage.

Steps to reproduce:

1. Build a high pillar.
2. Place vines/ladders on it.
3. Summon the mobs listed above on the vine/ladder.

Observed results:
The mob falls and takes no fall damage.

Expected results:
The mob falls and takes fall damage or climbs down.
Depending on the intended design. See MC-176379

Code analysis:
Code analysis by JingyBreadMan can be found in this comment.