Doubtful. Short of some radical technological revolution (for example, megawatt combat lasers, requiring high volume of fire from multiple autoloading cannons to saturate defenses), the coastal gunfire support could be achieved by other means.
For example, look at modern warfare; both Russia and Ukraine use high-precision glide bombs as fire support weapons. Including as heavy, as 3-ton ones (FAB-3000). Basically, those bombs replaced old-fashioned siege artillery in trench warfare.
For coastal gunfire support, I think, the analogue of GLSDB would be the most efficient weapon. With rocket engine from ESSM (we don't need ESSM sophisticated controls, merely the ability to loft the bomb on required altitude), such rocket-launched glide bombs could be quad-packed in Mk-41 cells. So one Mk-41 module (eight cells) filled with GLSDB, would provide 32 fire support weapons, capable of hitting targets at 150+ km range. With half of Arleigh Burke's cells filled with GLSDB, you would have 192 weapons.