I didn't think about the regulations side of it but I think it would be far less that the airspace restrictions since an underwater drone can't collide with an airliner or fall on anyone's head, plus underwater you can't really annoy anyone by buzzing around their heads. Of course I have no doubt some local governments would still find a way to regulate/ban them regardless if they started getting popular.
There are some
underwater drones already for consumers/prosumers at a reasonable price, but of course none can fly. I can see the camera being a real challenge as well, few natural bodies of water that I have seen are clear and drone cameras have a hard enough time in bright daylight, I can only imagine the problems in murky water.
Controlling it would be a real challenge as well, I think all of the current underwater consumer grade drones are tethered to the controller via a physical wire. I have had signal loss just dropping down to a few feet above the open ocean, can't imagine diving in on top of that.