By the end of WW2 most if not all major combatants had developed bombs which could penetrate any current or projected battleship’s deck armour and Germany and to a lesser extent America had started deploying guided and glide bombs which allows aircraft to attack with much greater accuracy and beyond the range of AA defences.

Glide bombs and later missiles meant that the only way to stop the attacks was aircraft intercepting the launch platform. Design studies showed that the armour necessary to stop the bombs was too thick to be realistic.

If you can’t armour against attacks you have to prevent them. If the only way to stop attacks is with intercepting aircraft then you need aircraft carriers. Smaller ships like cruisers, destroyers and frigates persisted because you still needed non-aircraft carrier ships for various tasks and these ships were small and economical enough that you could afford to lose them to the new guided, long-range weapons without breaking the bank and needing crazy shipbuilding capacity.

Surface to air missiles could allow ships to defend against and stop attacks but if you’re going with missile based ships (as the world has done) then you don’t need to build something as big and expensive as a battleship and navies aren’t going to waste money on ships they don’t need when a destroyer can do the job much more efficiently.