When would carriers finally displace battleships?

Where is the point at which navies stop building battleships in favor of carriers and large missile cruisers?

Probably in the 1960s, after battleships first shift into defensive, escort, and bombardment roles and decline more gradually than they did historically.

Without World War II's decisive carrier demonstrations, battleships retain institutional and symbolic weight much longer. They would first shift from primary offensive weapons into task-group air-defense, escort, bombardment, and status roles. Numbers may decline during the 1950s, but one-for-one replacement probably does not stop until the 1960s. Better air defense and guided-weapon refits could keep a few useful alongside carriers, especially if a later war validates the combined formation. The transition is gradual and driven by changing roles rather than a sudden declaration that the type is obsolete.