Our cat catches birds and rodents about equally judging on what he leaves at the door. I really appreciate that it catches mice and rats. It's unfortunate with the birds, I try to make up for it with a garden where they have ample opportunity to nest and find food.
Here [1] is what our "clown collar" looks like. It's just a loop. There's a hook that keeps it closed, but it's almost impossible to open it while it's on the cat. It sits so snug around the cat's neck that it never gets tangled in anything, and can't fall off, and we take the collar on and off just by pulling the whole thing over the cat's head.
My partner made this by sewing together some brightly coloured fabric with some shiny, reflective stuff.
Large hedges provide protection and the cats cannot get to the nests.
As for the other points, I suspect you're overestimating the dangers, but that's not my call. I personally think no animal should be kept imprisoned in a home, though; I don't want to give any animal less freedom of movement than I have. Imprisoned pets even more depressing to me than zoos.