I routinely do multiple hooksets, but mainly just fishing for smallmouth while dragging open hooked jigheads. Over the years I have discovered that smallmouth will sometimes clamp down so hard on your bait, that the initial hookset will not even move the bait in their mouth. The result of this is having the bait fly out of their mouth the first time they break the surface during the fight, all they are doing is opening their mouth. So for years I have been setting and resetting the hook during the early stages of the fight and have lost fewer fish because if it. If the fish becomes unbuttoned as a result of this multiple hook setting, you probably weren't going to land the fish in the first place.
The power of their mouths proves itself over and over to me too. Just last month I landed a small 2 pound smallie on the Niagara River that only had the dropshot weight in its mouth. The first time it took air and opened its mouth, my net was already under it, so I caught it. This happens A LOT with tubes and football heads too. I always feel better about landing fish once they take air the first time, and I still have them on after that.
I don't worry about largemouth so much, but find myself resetting if I think I flubbed up my first hookset. Seems like I do this mostly with frogs and T-rigs.