Now, what if you had tiny collars for birds, and a great big invisible fence that surrounded your house like a bubble? So all sorts of birds could fly in and out of your residential airspace, but your own personal birds would be trapped! Trapped like rats in a poolhouse. They'd grow used to you, and would fly up to you on the porch and perch on your shoulder. Wouldn't that be absolutely twee and adorable? Yes, yes it would be. A set of sparrows that always lived on your property. You could make them a little heated birdhouse, set out seed especially for them in the winter months.
I love this idea, even if it seems inhumane.
And remember to spay and neuter your pets. Except for the birds, because then you wouldn't get to see little chicklings grow up with their tiny expanding collars.