Why battleship construction might persist into the 1960s

Without the Second World War, how long would battleships remain viable?

Probably into the 1960s or later, with carriers gradually supplanting them through range rather than close-range killing power.

As long as one major power builds battleships, rivals have reason to answer with their own. Soviet construction could therefore keep British and American programmes alive into the 1960s. The carrier's wide-area reach differs from the battleship's concentrated ship-killing power. The carrier wins strategically because its aircraft can attack from beyond gun range and make repeated attempts, not because a battleship is harmless in a close surface fight.