If anyone had kept up with news, or history, they would have found the Sea Orbit where Enterprise (Carrier), Long Beach (Cruiser), and Bainbridge (Destroyer) circled the earth without being refueled because they were all nuclear powered vessels that were built in the 50's, and retired in the 70's. As such, refitting an Iowa class would not be a problem. The only reason more cruisers and destroyers were not built is because it was not cost effective, and the vehicles would not last 50 years like a super carrier would. The maintenance of the Iowa was also not cost effective, and that is why they have been retired (Even though they are retired and are museums, they are kept in working condition in case they are ever needed again). The Iowa Class Battleships were in service for more than 50 years, so it might be cost effective in the future if a new Battleship were built, but cruisers fill the gap having a smaller footprint, and firing missiles instead of the big guns. I like you, would like to see a BBN-81 Arizona in our future.
Nuclear power would be necessary for railgun turrets. You worry about cooling issues for the barrels, but those barrels will have cooling jackets filled with at minimum water, and more likely nitrogen. Even with water, the barrel would cool in a second or 2. You also have to think about what a Battleship would have. It would have 3-4 turrets with 2-3 barrels each. If cooling cycle is 6 seconds, then a Battleship could put in the air, 30 sabots per minute, and if my estimates are right, then it could put 360 sabots in the air. Actual will be somewhere in between.