I think bowhunting turkeys is a regional thing. I know a lot of turkey hunters...almost all hunters here turkey hunt, and I don't know a single one who bow hunts them and the few conversations I have had with people who hunt turkeys here about hunting with anything other than a shotgun has been "take a crossbow".
There may be some private land vs public land component too. My buddy who got me into turkey hunting always says "you can't hide a turkey". On public (and private too to a large degree), if one gobbles you are going to have every dude within earshot converging on your location with a shotgun in hand. That just makes it really difficult to get one with a shotgun, much less a bow. On BIG private, where the bird can be out of earshot of the neighbors, I would be considerably easier. A lot of folks don't acknowledge property lines when it comes to turkeys. I know guys who will cross property lines in a heartbeat if they hear a gobble. They own land and would be ready to kill anyone doing that to them. They see the inconsistency in that, but it is like an addiction.