I've killed several with three different 16 gauge guns, some with a Browning Sweet 16 loaded with #7 1/2 dove loads. Get the birds under 30 yards, and it really may not matter much what you're shooting.
IMO, it's mostly marketing hype that we NEED dedicated turkey guns with super-tight chokes.
Although I've killed most of my turkeys with a 12 ga gun, I expect most of my future harvests will be with my latest "dedicated" turkey gun which is a 20 gauge. Light as a feather, very effective to 45 yards, a pleasure to carry.