Mob Passive Regeneration

I just hate seeing a pig or villager randomly just die from a 4-block fall. I also don't like having to heal parrots with potions. Animals are not like a piece of tinfoil which can never be straightened once it has been crumpled. In general the health generation should be able to keep a mob that generally stays out of trouble alive but not enough to affect combat, something like one hp every 1200 ticks

Of course undead should be excluded. Some mobs like horses, foxes, etc. could regenerate health by eating readily available foods like grass or berries, while some, like fish, simply have a slow regeneration. By corollary, sheep and similar mobs should regenerate health like fish when mobgriefing is set to false. The point is, if animals are to have unique regeneration systems, make sure they are both renewable and require no player action.