“Out of sight, out of mind”
What you’re suggesting would not work for me, but then again, I’m not you.
I would find it hard to make time to go off-site to care for chickens, and would prefer the convenience of having them next to me.
Even if you get permission, and legally the city allows it, and the neighbors are OK with it, and it’s protected from predators, what about vandals? Bored teenagers with a mean streak? Other angry neighbors that might sabotage your coop?
Just an example of how petty people can be... my mom moved out of her house with her two small dogs and bought a condo a few cities over in a more affluent area. Right after moving in, while out walking her dogs in the complex a friendly neighbor chatted with her and kept petting her dogs around the neck.
Three days later there is a note on her door from the HOA saying she will be fined for not registering her dogs in the new city and if she refuses she’ll have charges pressed against her.
Her dogs were registered in the old city, vaccinated, and well behaved, and she always picks up their poop. But Mr. “Friendly Neighbor” noticed the dog tags were a different color than what the current city issues, and immediately went to the HOA to threaten fines and imprisonment. Petty people will do petty things.