Should the 21st-century battleship use nuclear power?
Short answerProbably not for the main ship, though a small reactor might be useful in a secure separable pod designed to carry the crew away from a lost vessel.
NotesNuclear reactors are a doubtful choice for a ship intended to enter heavy combat. A narrower possibility is a secure internal pod that could separate from a disabled ship and shelter the crew during their escape. A small modular reactor might let that pod operate underwater while leaving the area. This remains a conditional suggestion for an extraction platform.