well, if well decks and davids had the same use circumstances, then ships damaged in storms would be in big trouble, because all the lifeboats are in davids. no, it is not perfect, nor comfortable under those circumstances, but you can safely use them a lot more then well decks or bays.
Ships damaged in storms "launch" ie toss over the side cannister inflated lift rafts and board them from the water once they themselves heave over the sides. It's an uncomfortable truth but ships in a storm back when winch and davits the sole means of having life boats more often than not went down without using them for this reason. "All hands lost" was a common headline.
launching them is possible under almost any circumstance, recovering is a bit harder. but, you don't go into seas from the coast to the hospital ship under those circumstances with patients, you might want to leave the ship (for rescue or anything like that) but you won't tackle the boats on board.
I suppose modern hard hulled life boats on some merchants operate on this concept, they are pretty much capsules designed to survive all seas and are also pretty much dropped over the side which must be one hell of a ride.
But like you said hospital ships are most concerned with getting patients on, not off. By their nature they arrive after a disaster not during unless they are acting as a military hospital. In all likelihood patients would be helicoptered on by any modern nation fielding such a ship and the well deck would probably be mostly involved with moving medical vehicles and stores ashore. Unless the place is completely screwed up where you can't just find a place to dock or land helos the well deck is probably not going to be the first choice in patient loading. That's actually one of the biggest critisisms of the Mercy class, their inadequate aviation facilities.