I wonder how much it would cost for some very rich person to build a modern, heavy armor battleship with 16” typical range rail guns. Here’s the logic.
To start with, modern anti-ship missiles are designed to attack very light ship hulls. On the typical ship they are devastating, but would hardly scratch the paint of a WWII-era battleship. However, armor today is much, much better than it was then, as well as much lighter, so a modern heavy armor battleship would be far harder to kill than even a WWII ship.
Add to that a typical 16” HE round, but not propelled by powder, but by a rail gun. Naval rail guns are designed to propel very small projectiles at extreme speeds over vast distances, but similar technology can heave a heavy projectile about the same range and speed as powder, but much more safely.
But why do such a thing?
For a very good reason. Coastal bombardment, which today is done with cruise missiles and other high tech toys, is very small and precise. However, sometimes you do not want precise. You want a sledgehammer.
And nobody who has ever experienced a US Navy 16” round has ever forgotten it. It can pick up the side of a mountain and shake it, hard. No finesse is involved. Importantly, no one who has ever experienced this wants to experience it again.
And that can be very useful in war.
Torpedo beneath the hull will break her back. Unless the armor is exotic stuff like the frontal armor on modern MBT's, even relatively small shaped charge warheads will easily punch holes through traditional thicknesses of rolled homogeneous armor plate on battleships.