Early anti-ship missiles and battleship survivability

If the Second World War began in 1947 with anti-ship missiles, would battleships lose value to small vessels?

Not automatically; larger ships could survive more hits and carry heavier weapons, while small ships would remain more vulnerable.

Early anti-ship missiles would let small vessels threaten capital ships, much as torpedoes already did. That offensive reach would not erase a battleship's greater ability to survive multiple hits. The larger hull could also carry more weapons and heavier missile systems than a small combatant. The result is a new tradeoff in reach, magazine depth, and survivability rather than an automatic transfer of value from battleships to the smallest ships.