Were battleships obsolete after 1945?

Did battleships become obsolete after 1945, or were they still useful but too expensive?

They retained useful specialist capabilities, but carriers offered broader value, making battleships difficult to justify in a reduced fleet.

Battleships were not obsolete if the word means they could no longer fight or provide distinctive heavy firepower. The problem was that those useful capabilities had become narrow compared with the carrier's adaptable reach. A shrinking navy had to fund a large crew and expensive hull for missions other ships could cover in part, while a carrier could support many different operations. Postwar retirement was a force-structure choice about value per resource, not proof that every battleship capability had vanished.