Littoral ships do that for much cheaper.
After tuning the tech and increasing production numbers, drones will be more affordable for inland small ops targets. Which makes much smaller drone carriers viable.
There is realistically no place for conventional battleships at present.
Once we have strong railguns, they will have a role for sustained barrage fire, but they will require nicer AA/sub screening ships, otherwise they are much too vulnerable.
This is all assuming we don't go the heavy distributed support direction like we have with our airforce; which would look something like a primarily electric craft,
composing of single railgun destroyers, ultralight drone carriers, and nuclear generator ships **** with additional detection/comm eq) to fuel the rest. The obvious hole here is AA, but current ACCs with fielded with something much better against sukhois than JSFs; ie dedicated AA craft. Current DARPA R&D points to light laser strikers with heavier BVR missile support. This strategic direction has the advantage of requiring very little resupply, along with deployment flexibility.
A litoral ship is designed for close in shore work. attacking pirates in somalian waters, spraying beaches with small arms, etc. It's the modern navy equivelent of a frigate, both in size and in throw weight. A 2.5 inch gun is a popgun compared to a 16 inch battleship shell, and a littoral ship is essentially useless as a shore bombardment platform unless you include their missile capability. Even if there are more drones, they still fire very expensive missiles compared to a cheap solid chunk of metal. Though i agree that small drone carriers, probably built on an America/wasp class marine carrier hull are a given in the near future. But the point remains, a battleship is THE single most cost effective shore bombardment platform we know of. Even aircraft carrying dumb gravity bombs are more expensive simply due to expended fuel.
An iowa class battleship, retrofitted to modern standards with current generation engines (conventional or nuclear) wouldn't be all that vulnerable. You could actually get about 20 CIWS Phalanx mounts on the old Bofors 50mm antiaircraft mounting points if you really wanted, which would make them very difficult to hit with missiles. Radar signature would be a problem unless they did a redesign of most of the topside and a recoat with radar absorbing paint, but you generally don't try to hide a battleship anyways, and in a shore bombardment role, we already control the immidiate sea area. Torpedos would be a problem, though i'd probably retrofit the battleship with stabilization pontons to allow for larger guns and higher muzzle velocities and use them as anti torpedo blisters of a sort. Between that, and the kinds of reactive armor we can build these days (see the M1-A2 Abrahms) means it would be very difficult to kill a battleship short of a nuke, and if we're talking nukes, our entire fleet is vulnerable.