The pan of water moderates the temperature of the cheesecake. Without it, the outer edge tends to over cook and become crumbly. Also by moderating the temperature of the cheesecake, it limits oven spring to a degree. Not as much lift so not as much fall.
But really, a cheese cake should fall some. Cheesecake should have a density to it. While something lighter and airy and taller has some appeal of it's own, it's something different from cheesecake. imho.