When I trained pointers and hunted bobwhite I started with a 20 gauge 870. It wasn't uncommon to kill five birds on the covey rise. But you fill a limit too quickly that way and your hunt is over for the day. After I switched to a double I would concentrate on killing two birds on the covey rise and then hunting the singles. That was much more fun and extended the hunt and the training.
Without a dog to retrieve, the third shot will cause too many lost birds. It's just difficult to mark three downed birds and find all three.