Battleships were more vulnerable in WW2 than they are now. In WW2, most weapon systems were designed to be able to take out a battleship - and the effective air defense range of a battleship was only a few hundred yards. More on this later.
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Modern missiles aren’t typically very big, and almost all of the space on the missile is used for fuel. The actual warheads involved are actually pretty tiny. This is fine for taking out unarmored cruisers and other modern naval ships, but they simply weren’t designed to be able to damage a battleship.
Modern naval doctrine has practically unarmored ships in favor of the idea of not being hit… they’re not designed to take a hit, and so the weapons designed to kill them aren’t very powerful.
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Actually, battleships typically have stronger armor on their decks than their side - most naval gunfire comes in at a high arc, ‘plunging fire’, so in the design the deck was heavily armored.
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It would fare better, but that’s a valid concern. Firstly, though, there are very few of the really large antiship missiles out there - predominantly there are small, cheap ones.
Secondly, the bigger, slower missiles are much easier for any given naval group to destroy at range so they don’t become a clsoe threat.
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I’ve never seen it, unfortunately 
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Well, the first part is true. But I doubt a new country is going to spend money to design a new cruise missile for the specific purpose of taking out ships that we have only perhaps 2 of (if we recom some).
Secondly, they’re really not all that expensive. They’re already built and upgraded - there’s only the operations costs to worry about. Also, much of the upgrading computerized systems allowing for less crew, and so the battleship only requires about 1/4th of 1/3rd what a carrier would. Other costs are typically 1/3rd of a carrier, too. It’s really not that expensive.
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As I said, weapons designed to hurt small, unarmored ships (the vast majority of modern day antiship missiles) aren’t going to do serious damage to a BB.
Also, anyway, the whole naval concept these days is not to let any missiles get within miles and miles of any naval task force - and the battleship would afford equal protection under that umbrella. It’s unlikely that a missile would penetrate that shield - but even if it did, like I said, the BBs can take a hit.
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Tell that to the marines who have to fight without any real artillery support.
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Ah, cool.