Could long-range gunfire keep battleships relevant?

Would rocket-assisted shells and later guidance systems extend the usefulness of battleships?

They might, if their range, accuracy, and cost compared well with missiles; the result could also alter how carrier groups allocate aircraft.

This is a cost-and-effectiveness question rather than a simple survival of the battleship. If guns became cheap, accurate, and sufficiently long-ranged, they could retain a useful fire-support role. That could shift carrier aircraft toward longer-range strike missions instead of routine on-call support.