CBG has all the elements required to mount an attack as well as be able to defend it self and the ACC. The complement of aircraft that the carrier carries also protect their base.
IMHO, with the growing naval air power, MiG-29ks and Naval Tejas and other aircraft in the inventory, IN should shoulder the responsibility for maritime security, while IAF should do what it does best - defend the skies where needed.
The USN operate their own air-wings, along with the marines airwing and USAF does not interfere with their responsibilities.