Would the major navies eventually retire every battleship?
Short answerNot necessarily; a few could survive as status ships and carrier-group escorts, especially if modernized battleships perform well in a later war.
NotesThe battle line would probably contract, especially from the 1960s, but some major navies might retain the type. A few modern ships can remain potent symbols of national power even after carriers take the main offensive role. If improved air defenses and guided weapons let them operate successfully with carriers in a 1950s conflict, they gain a fresh operational case as well. Without the historical Pacific watershed, prestige and battlefield evidence could keep a small residual force in service for much longer.