Excuse me, that was carriers CANNOT engage in gunfire duels...
At the close of WWII, the Navy had built the Alaska class battleship, which was faster, better armored and more stable than the Iowas. They were the Alaska, Guam and Hawaii. None was ever cokpleted because the conventional wisdom was that air power made the battleship obsolete. Had they been built, it's quite possible they would have fired the opening rounds in Desert Storm.
A follow-on to the Iowa class was the Montana class battleships, all of which were scrapped before the war ended. These ships were to have double the AAA capability of the Iowa while still retaining the 16" guns. These ships were believed to have been constructed specifically to take nuclear power plants, if and when they became feasible. The older oil-fired or electric turbine systems (whichever they would have used) would simply have been replaced with a nuc reactor.
Also, the last battle ship built was the Russian Kirov class, in the 1970's, which is regarded as more of a battle cruiser. It used anti-ship missiles in place of a main battery of guns and was nuclear powered.