To me, it's not entirely clear why we're bothering. Do we actually envision shore bombardment as a useful combat modality going forward? IIRC the types of ships that can mount this weapon are the same types that are currently vulnerable to hypersonic anti-ship missiles. All our potential equiv-tech adversaries have those, to my understanding. So wouldn't the railgun only be useful against lower tech opponents? And against such opponents, does it fill a substantial gap where we don't already have sufficient other tools?
A large part of the reason that guns fell out of use on warships was that they were outranged by everything - guns that can shoot up to 40km (like those on the Iowa class) aren't enormously useful against destroyers tossing missiles from 200km or strike aircraft from a carrier 400km away. Guns that can shoot down planes and incoming missiles at 100km, though? That's pretty damn useful, even if it doesn't close the distance entirely vs missiles. As for why guns at all - well, guns tend to have magazine depths undreamt of by missiles, and railguns will likely follow that pattern. If moving to railguns for AA defence means you can shoot down 3 or 4 times as many incoming missiles for the same weight, that would be enormous.
And in the fog of war... Who's to say that a DD won't be able to close to railgun range of an enemy warship? Life's a lot easier when you can stay below the horizon, after all!
There are no hypersonic antiship cruise missiles deployed today. Some ballistic missiles have limited antiship capability and they do travel at hypersonic speeds but there are reasonably effective defenses against them now.
The railguns can be used to shoot down missiles. Interception is a matter of speed. If railguns are faster they win and we are back to fighting with bullets.
