The defense problem with carriers lies in the inability to reload VLS systems at sea. If you can catch a battle group far enough away from port and saturate it’s defenses eventually it’s going to run out of SM-2’s, Sea Sparrows, etc. to stop incoming missiles.
Actually the problem is that CVBGs now have 3 escorts. They used to have 2 Destroyers, 2 firgates, and 2 or 3 cruisers. Now they are lucky to have 2 Arleigh Burkes and a Ticonderoga.