The opening problem is whether battleships became obsolete or simply lost the mission that justified buying them. Super-battleships demanded exceptional amounts of material and money while carriers, submarines, escorts, and other smaller warships competed for the same resources. Fleets urgently needed those smaller combatants, which made every new battle line a costly decision about resource allocation. Battleship decline therefore depended on expected missions and procurement priorities as much as on vulnerability to another weapon.
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Why battleships fizzled out
Battleships declined after 1945 because navies lost a compelling reason to buy them, rather than because their combat power suddenly vanished.