It's probably to limit the number of living things around the house, and avoid performance issues/bugs. It can get crowded there (chickens, cow, horse, you, driver, family outside, housecarl, steward, bandits raiding your home, etc.
This is it exactly. Once you have too many NPCs, animals included, in a cell, things start to bog down.
Thinking about this, I don't know if I have even seen more than 3 Chickens at any farm or coop. Then again, I was not conducting a chicken census.