Could modern hypersonic or widely available supersonic missiles simply destroy the battleship?
Short answerThey could damage or eventually sink it, but layered defense and subdivision should require a costly multi-missile attack rather than one automatic kill.
NotesThe answer rejects the standard that a ship is useless if some weapon can sink it, because that logic eliminates every navy. Armor, subdivision, defensive missiles, and redundancy are intended to turn a single hit into damage rather than immediate loss. The relevant measure is how many scarce, expensive weapons must be launched to obtain enough penetrations for a kill. An attacker must therefore allocate a larger and more expensive salvo, while firing at the ship in peacetime would itself trigger the conflict its presence is meant to deter.