General Discussion

...the day someone invented an antiship missile that would penetrate their hulls.

Here's the thing: A battleship historically had two missions: sinking the other side's ships, and bombarding their shore fortifications. Both those missions can be more successfully done with an Arleigh Burke-class destroyer armed with several kinds of torpedoes and missiles. And seeing as how a Burke is far less expensive and requires far fewer personnel (like, one-tenth the number of crew that an Iowa-class battleship needed) to operate, you can put three Burkes in the water instead of one battleship...so, y'know, if the enemy manages to sink one you've got two others still prosecuting the enemy.