Biome borders for mobs

There are so many mobs that can spawn in so many biomes, which is why I think there should be something called biome borders. Biome borders would prevent mobs from randomly moving to one biome to another on it's own, the only way to get a polar bear to a jungle would be by a lead or a boat. This would give leads uses as they would be the only way to transport certain animals. Also with animals in the next update that seem to only live in certain conditions, would most likely die in real life. Pet should still be able to follow you any ways, as a cat can still live mildly cold areas, same for wolves.

With hostile mobs it would be like drowns, they go back into the ocean in the day, but instead they go back to their certain biomes after you leave them or they follow you too far. You wouldn't find a husk in a neighboring ice plains would you? I can see biomes borders as a adjustable command as well, such as how far can a mob walk away from it original biome or how many seconds does it take to die outside it's biome, like world borders. Biome border also has a catchy name :D