What an American 1980s battleship replacement might be

If the United States needed a new ship for the battleship role in the 1980s, what would it build?

An Iowa-sized, fast Aegis strike-cruiser type with missile launchers and substantial guns.

The imagined ship keeps the speed and broad scale associated with Iowa rather than reproducing a 1940s battleship unchanged. Its defining feature would be an Aegis or comparable air-defense suite integrated with missile launchers. Heavy guns would remain because the requirement is specifically to fill the battleship role. The result resembles the strike-cruiser concept enlarged and armed for sustained gunfire support.