Why a warship cannot simply power a damaged city

Could a nuclear-powered hospital ship supply electricity after a city's power plant was destroyed?

Only with compatible port and grid infrastructure; in most disasters, local generators and grid repair are more practical.

A ship may have ample generating capacity while lacking a compatible connection to the local electrical network. The port must accept the vessel and have shore connections that can carry the required power. Shipboard voltage would also need conversion to match the local transmission system. A disaster severe enough to remove every normal supply may have destroyed the grid needed to distribute imported electricity. Lexington-class assistance is recalled with uncertainty about the location and circumstances, while Russian nuclear icebreakers provide another example of supplying shore power where supporting infrastructure exists. Portable generators for critical facilities can be easier to deliver. One hospital described from personal experience tests its diesel backup weekly and keeps fuel estimated to last a couple of days, making fuel resupply a practical immediate priority.