Nuclear cruisers as carrier escorts

If more nuclear-powered Aegis cruisers had been built, how might they have been used?

They could have formed the nuclear-powered core of carrier groups, keeping pace with carriers while other escorts supplied the outer screen.

Building enough nuclear cruisers to assign roughly one to each nuclear carrier group has a clear operational logic. A carrier and cruiser would form the long-endurance core, with conventional Arleigh Burke-class and other escorts around them. The nuclear escort could keep pace with the carrier without sharing the same refuelling constraint as the outer screen. Cost still prevented such a fleet from becoming the historical US Navy force structure.