Battleships were actually obsolete by the onset of WWII, the world's navies just had not realized that yet.
Modern technology could deliver killing blows to the heaviest armor from a hundred miles away. Various encounters, like Pearl Harbor, the Battle of Midway and the hunt for the Bismark, made that clear.
Take the USS Arizona, blown up at Pearl Harbor by what was essentially a 16-inch shell turned into a 800kg bomb, carried into the defensive fire by an expendable resource (a.k.a. dive bomber)...
So why bother with slowing down your vessels, reducing their operational range, for a "protection" that was marginally useful against something that was on its way out (ship guns), and was useless against what was used now (bombs, and later, missiles)?
If an enemy air threat made it through SAM and point defense fire, no reasonable amount of armor protection would save the ship.
So, trade the armor for mobility, operational range, and defensive armament. (Stealth came into the picture as well, later on.) The result of this development was the modern missile cruiser.
A similar development took place on land as well. Modern AP ordinance made heavy armor useless, so heavy tanks were abandoned for tanks like the German Leopard 1, forsaking armor for speed, agility, and firepower.
While composite armor made heavily-armored MBT's a viable option again (in part because they have some kind of choice which way they will be facing the enemy), the song had ended for heavy armor at sea. You are too much of a target, and too easily sunk, regardless of the thickness of your belt or barbette armor.