Turkey? No. Too heavy, way too heavy. Early in my turkey hunting career I used a BPS 10ga but it was clear that I could do much better. A good turkey gun is light weight, camo, and has a short barrel. My BPS 10 was none of those things.
Ducks? No. Too expensive, too heavy, too slow. A box of steel shells for a 10 are substantially more than a box of 3" 12ga. The weight of the gun also makes it slow to swing and somewhat poorly balanced. Plus the extra long pumping stroke makes the gun slow to shoot. For veteran 3 1/2 12 ga guys maybe this isn't a problem, but I'm not one of them. I don't see the need to shoot 3 1/2" 12ga shells for ducks. Also I've never seen waterfowl loads in shot smaller than 2s.
Geese? Yes. This is why I still own my BPS 10. Simply put 10ga 3 1/2 BBBs are a lethal load for canadas. Could they be killed with a 12 instead? Sure, but any veteran goose hunter will tell you that a Canada can take an impressive amount of shot. The extra pattern density and knock down power are worth the work. Plus the major downsides don't apply as much when goose hunting. Usually you don't have to carry the gun that far and the shooting isn't as fast.
As for slugs? No clue. I've never seen a 10ga slug and I can't make a judgment. Seems like something someone would do more because of novelty than usefulness.