Carrier is good for sea domination and attack far away enemy targets but the problem is that since its carrier based plane, but range and the load is limited due to not putting too much stress on air frame.
Also lets assume Indian navy carrier based plane attack Pakistan, surely their planes would chase the retreating planes. Now the PAF would be able to put more planes in the air than a carrier., So what do the retreating planes do? Dump themselves in the sea or return to carrier and hence give away its position? Remember the carrier will be limited by numbers and PAF knowing these are carrier planes, will firstly put on more nos in air and also know that these planes will return to the carrier and hence it puts the carrier group and the carrier at risk.
Carrier group is useful if you are able to project more (twice ) the nos of planes as compared to enemy. And in the example you gave, we would not be able to do so. We can do that for bangladesh, sri lanka or Seychelles or Myanmar but not China or pakistan.
The Americans were successful in Gulf war not due to carrier but their Saudi based USAF was able to put more planes in air much more than what Iraqi air force could put. Let us say we are in war with Pakistan, when actually would you use to strike targets in Pakistan? you would be targeting Islamabad? No... you would be targeting Karachi.. yes, Karachi can be targeted by Land based planes.. Are you going to use Carrier against Chinese assets in south china sea? No.. where exactly would you use it? Please give me a real life example where you would use carrier if you are indian admiral, lets see your example