There was a scenario up around Iceland in the old naval DOS wargame "Harpoon" that gave the NATO side a surface action group with a couple of Iowa battleships as the core. Plus a carrier strike group as well. IIRC, the Soviets were invading Rekyavik or whatever.
The scenario was really quite simple - you let the enemy AI know where you were by having some destroyers appear near the invasion force where radar helos would detect them. He would send all the land based backfires at them, you then murdred those with the F-14s and proceeded to find the invasion force and bomb it to bits with the strike planes since carrier air in harpoon had infinite supplies of all air launched weapons, so why use the dumb bombs etc when you can have all the harpoon SSMS...
Therefore your surface action group with the great big battleships was actually quite superfluous.
However - if you voluntarily held off with using the carrier strike group (other than to clear the skies of backfires, bears and recce helos) then you could charge the SAG into the middle of the Soviet landing group and have sheer fun blowing sverdlov cruisers away with your Iowas. That was rather satisfying
!