Well... current missile technology would allow for battleships to have a much better defense against aircraft, the problem is the way armed conflicts have evolved, there isn't a high need, if a need for it. Not to mention it wouldnt be cost-effective, since it would only have a range of a few miles inland. AC-130s, A-10s, Predators, along with B1 and B2 bombers have made whatever role a battleship would have unnecessary.
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