I have always used a 410 ga # 4 shot , 20 ga # 6 shot, or 12 ga #6 shot for all small game , like rabbits and squirrels. My Father did the same thing and wouldn't let me use a 22 for squirrel, because what goes up comes down,,, someplace...
My son uses a shotgun for small game and my grandsons do too.
We got a couple AR rifles too, but just like tools, different job may require a different tool. We got one AR-15 set-up , scoped for coyotes and varmints.
We don't eat the varmints, but all the other small game goes in the pot.
We got an AR-10 7.62 mm with a 1.5 X 5 IR scope for close up pigs in the creek beds. We got regular bolt action rifles for deer that are scoped, for the job to be done.Catch my drift.
If you ever want to go small game hunting with us sometime, let me know, and we have an extra shotgun for you to use. Its great fun..