Why rapid-fire eight-inch guns do not make a battleship

What is the smallest useful autoloading main-battery calibre for a battle-line ship?

Eight inches remains too light against battleship protection, however high its rate of fire.

An eight-inch autoloader could produce an impressive volume of fire. The opposing battle line, however, would be protected against 16-inch shells and much heavier weapons than an eight-inch gun. Rapid hits cannot compensate if each projectile lacks the penetration and destructive effect required against the target. Calibre and target protection therefore remain hard constraints on a rapid-fire battle-line weapon.