[MC-176379] Climbing of animals on ladders is inconsistent

The bug

When any living entity falls into the space of a ladder or vine block, their fall distance resets and they 'climb' down the ladder/vine. For certain entities, such as players, endermen and zombies, this is consistent. For entities like pigs and sheep this is not consistent though: real pigs and sheep can't climb ladders, neither up or down.

A more consistent solution would be to separate living entities in those that can climb and those that can not climb:

What entities should definitely climb

Player
Cat
Ocelot
Snow Golem
Villager
Wandering Trader
Enderman
Zombie Pigman / Zombified Piglin
Spider
Cave Spider
Iron Golem
Creeper
Drowned
Evoker
Husk
Pillager
Skeleton
Stray
Vindicator
Witch
Wither Skeleton
Zombie
Zombie Villager
Piglin

What entities should definitely not climb

Cow
Donkey
Fox
Horse
Mooshroom
Mule
Parrot
Pig
Rabbit
Cod
Salmon
Sheep
Skeleton Horse
Squid
Tropical Fish
Turtle
Pufferfish
Bee
Dolphin
Llama
Panda
Polar Bear
Wolf
Blaze
Elder Guardian
Guardian
Phantom
Ravager

Other entities don't really make sense whether they do it or not.

To reproduce

Place a column of climbable blocks
Spawn a pig on top of the column so that the pig falls down
See the pig climbing down: pigs can't even climb...