In the first Desert Storm some Iraqis learned that the little unmanned drone plane was used as target spotting for the battleships. There is video of the Iraqis surrendering to that unmanned plane. Apparently bombardment from a battleship is psychological leagues past having a 2000 lb JDAM dropped on you. A corollary to this was in Afghanistan in the early days when we got there. Apparently there were some diehard fighters opposing us and all the smart missiles we threw at them did not dislodge them. They then had a B-52 carpet bomb the area and that was that…they gave up. Point being sometimes just a massive amount of ordinance can do things smart weapons cannot.
IIRC at some point during the Korean War we wanted to get the North Koreans to the negotiating table and they were refusing. We sailed (I think) two battleships off their cost and they positively freaked and said they would come to the table if the battleships were removed.
Further, battleships actually had some of the best if not the best hospital facilities in the fleet. I think the US only has one dedicated hospital ship currently. When you are on the front lines (or near enough) to the battle having a capable and large floating hospital close at hand is a good thing.
Add to that battleships are floating machine shops. Granted in this day of electronics that is somewhat less useful but the battleship was the closest thing to a mobile factory as you got. It was capable of manufacturing new parts for broken stuff (which happens a lot in war) on site. No need to wait for FedEx to deliver.
I also think people are underestimating their survivability. Yes a modern torpedo would likely nail one but then that is true of carriers too. We have assets in place to stop that (attack subs, frigates). Not too many countries can even field a respectable submarine force. Modern missiles would almost certainly just bounce off a battleship. A single Exocet sunk the HMS Sheffield by striking her amidships. The USS Stark took two Exocets and was badly damaged. A battleship would have largely shrugged both off and remained operational. Add in proper fleet defense and a battleship is very survivable. Consider the absolute pasting the German battleship Bismarck took and, while a smoking wreck by the end of it all, was actually still afloat and likely scuttled by her crew.
The above from my previous post: http://boards.straightdope.com/sdmb/showpost.php?p=10864377&postcount=151
The Japanese battleship Yamato took 10 Torpedoes and 7 bomb hits to sink (380 planes went after it). Nothing is survivable when you try that hard to sink a single target. Can any military throw 380 planes at once at one target today?
In addition to above think of the battleship as a mobile artillery platform. Ask any marine if they’d rather have a drone with some missiles at their back or artillery when attacking a position. If you are trying to land troops on a defended beach there is probably nothing better than a battleship to have at your back.
Granted BB guns on an Iowa Class can’t hit that far but point being there is plenty within range of their guns. IIRC (and I may be wrong) during either the Korean or Vietnam war sending a battleship up near their coastline was enough cause the opposing side to agree to come to the negotiating table as long as the ship was withdrawn. They are terrifying if you are within range of their guns. Terrifying in a way no missile cruiser can be.
Add in that shells are comparatively cheap A Tomahawk Cruise Missile costs over $1 million. I’d be surprised in a BB main gun shell cost even $10,000 but let’s say they cost $20,000 each. That is 50 shots per one Tomahawk. Starts looking costs effective and it can shoot all day long rather than what…a few volleys from a missile cruiser?
All that said Battleships are incredibly expensive ships to build and require a massive amount of steel (as in a substantial percentage of a big country’s yearly steel output). I would also imagine a modern one would be nuclear powered.
If we had anything like a WWII scenario where we had to make regular invasions via beaches then a BB would make a lot of sense. I do not think we live in that world anymore though.
They may not even work as a means to instill terror because I doubt few alive remember what it is like to be pummeled by one. No one would know enough to be pissing in their pants.