Why quadruple 16-inch turrets create punishing design tradeoffs

Would quadruple 16-inch turrets make sense for a Nelson-class follow-on battleship?

The mountings would make the ship very broad and place severe stress on the design, while a triple 18-inch turret could use roughly comparable space.

Four 16-inch guns in one mounting would produce an exceptionally wide turret. The mounting would also place severe stress on its mechanisms and the ship built around it. A triple 18-inch turret could occupy roughly comparable space. That comparison weakens the apparent economy of adding a fourth 16-inch barrel to each turret.