Missiles weren't what killed the battleships, cost did. The cost of manning them, and the cost of the support vessels to get them close enough to use their primary guns. Battleships are still markedly more effective at killing other ships and land targets, but they have 1/10th the range of a missile...
Battleships also have little to fear from missiles themselves, it's mines and torpedoes that were the concern. When I was deployed in the Gulf on USS Wisconsin, the danger of shore or aircraft launched missiles was trivial compared to the worry of hitting a mine.
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