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Technically the caliber of the gun is only secondary to the objective to cause damage and more precisely where on a target. 12 inch is considered a heavy caliber and should be treated as such, making it very much capable of inflicting damage to all sorts of targets. (the German 11 inch/54 cal was treated simmilarly for obvious reasons.) Even smaller calibers can still cause damage to a ship, but are propably insufficient to cause critical hits.

the USN 12 inch shell for the Alaska's was smaller and weighted less than a battleship caliber gun, but was large enough to cause damage on any sort of ship, although propably not capable of penetrating heavy armored decks or belts. All other structures could be damaged, so it was in a way as good as any other gun. For example a 6 inch guncruiser at close range can completely cripple any BB with her fast firering guns, but not sink it outright (unless it can use torpedoes.) The 6 inch shell is powerfull enough to damage unarmored and lightly armored structures and the shell even has potential in armorpiercing, altthough not the most heavy ones. By knocking out all un- or lightly armored structures on a battleship, including its capability to fight back, it is neutralized, although not sunk. Alaska could do a simmilar jobe as well, although with less higher rate of fire.