Originally posted by MrLars
I'd bet that all you'd do is create a larger ack umbrella for the pilots to hide in.
Forgot to respond to this part

This argument misses the point. CVs are an offensive weapon, intended to provide a close base near a key nme area for purposes of neutralizing and capturing that key nme area.
For instance, CVs about the best tool for attacking the country in the NW peninsula of the Mindinao map. If your country attacks from the center of the map towards the west along this peninsula, the attack often quickly grinds to a halt. This is because once you establish a foothold at the base of the peninsula, you have driven a wedge between the 2 nme countries so now your schwerepunkt has to fight a war on both flanks. This dilutes its effort to drive further along the peninsula. OTOH, you can take a CV group across to the west end of the peninsula to roll it up from the rear.
What this all means is that to be effective, forces from the CV have to leave the TG's ack umbrella to conduct offensive missions. If the defenders achieve enough air superiority to keep the attacking planes circling in the ack, then they have neutralized the threat posed by the CV group.
A CV with planes hugging the ack is useless. That's the important thing from the POV of your country's strategic situation. So consider such behavior a sign of success. Not only have you thwarted the nme's sea-based offensive in this area, but that TG can't influence events elsewhere.