You could; most antiship missiles aren’t really armor piercing, just really big and strapped to what amounts to a really fast moving small aircraft. Kind of like a kamikaze on steroids, in a certain sense. I suspect that no antiship missile would make it through the barbettes on an *Iowa (or anything after the North Carolina *class really)
But the armor’s not the point. The point of battleships like you and others have said, was to be the ultimate evolution in the line of battle style of naval warfare that started centuries ago with the development of the cannon. You know, the way that Nelson, Cochrane, Hull, Broke, Lawrence, Tromp, De Ruyter, Bart, Jellicoe, Scheer, Hipper, Beatty, et al fought.
Problem was, in WWII, the aircraft carrier had rendered that style of fighting hopelessly obsolete. What good were 16" or 18" guns with an effective range of 16 miles, if one of your enemy’s aircraft carriers can launch 43 dive bombers, each with a bombload of up to 2000 lbs, and 11 torpedo bombers, each carrying a torpedo? This was proven time and time again with the Japanese in World War II.
So what’s a battleship good for? In WWII, with the capital ship role rendered obsolete, they were used as extremely powerful naval artillery to shell enemy positions prior to, and during amphibious landings, such as D-Day, Okinawa, Iwo Jima, Saipan, etc… In this role, they excelled, since the 14" and larger guns pack a lot more punch than a destroyer’s 5" guns, or a heavy cruiser’s 8" guns. But they were only effective to a range of 20-25 miles inland at best, and probably not with much accuracy at that distance.
That’s also why they were scrapped or mothballed at the end of the war, and a couple were brought back to service during Korea and Vietnam. The only reason they were brought back into service in the 1980s was essentially because during the Cold War, we were willing to use just about any hull that would float, not because there was a legitimate surface warfare role for the battleship again.
In today’s navy, most of the surface warfare ships (i.e. destroyers, cruisers and the few frigates that are left) are predominantly armed as either anti-aircraft platforms or as anti-submarine platforms. In a sense, it’s the 1945 Okinawa strategy writ large, with 70 years of technological advancement. The cruisers and destroyers protect the carriers from enemy missiles and aircraft, and the carriers’ much longer ranged air wings go after the enemy ships, while the submarines do their own thing under the waves. Now whether or not this doctrine is still valid… who knows? But it’s likely that a battleship wouldn’t have a role in it or any follow-on doctrine.
So what role would a latter-day battleship fulfill? Shore bombardment? I don’t know that you really need a 16" gun for that- wouldn’t a terminally guided 8" gun do just as well> You wouldn’t need armor, as it would almost certainly operate within the aegis (heh) of some kind of battlegroup.
If the point was to close with the enemy and destroy their surface ships, you’d probably be better off with some kind of stealth ship that could get in close and fire, and then get away without being detected. Even there, I’m not sure what a surface ship in that role would offer that a submarine doesn’t already offer in the same situation.
There’s a good reason that nobody operates battleships anymore; they’re big, expensive and there’s no place for them in a modern navy.