What really killed the CGNs (nuclear powered destroyers) was VLS (vertical launch system) and AEGIS - the sensor suite that newer Navy destroyers and cruisers are built around. CGNs were all built around magazine fed rail-style missile launchers, and sensors were all designed when state of the art was a transistor. Refitting ships to modern sensors like AEGIS and modern VLS was almost a complete rebuild. Even early Ticonderoga class conventionally powered cruisers (CGs) that had rail launchers were retired early because of the cost of refit to VLS.
Incidentally, VLS allows for much faster deployment of missiles, and doesn't require deck space for different launchers for different missiles, and a ship with a modern VLS have a huge rate-of-fire advantage on older rail launcher equipped ships.