So far in the early game, my go-to strategy is to dig a 7x3 pit, about 3 or 4 blocks deep, near a forest and lure bears and wolves into it. It’s saved my ass more than once! I start hunting them with nothing but flint spears that I craft and place next to the pit trap. This works too well.
My suggestion would be to give animals a small chance not to fall into a 3-block-deep pit when they’re chasing a player.
However, if they’re right behind me (1–2 blocks), the chance that they don’t fall in should be higher. If they’re further away (6–10 blocks), the chance should be much lower that they avoid the pit.
Sorry for my English — hope it’s clear what I mean. If this has already been suggested, please close this post.