The reason IN has operated carriers so far are not really operational once. PN is no match for IN even without carriers, be it numerical, or wrt to quality, which is why PN will play it defensive anyway, except of their subs possibly. The close proximity of both countries makes naval attack not really important in a war, since our shore based assets are capable of taking out their naval and coastal targets too.
The reall threat comes from PLAN and primarily from their sub fleet, which is why the money we wasted on this carrier and it's aircraft would be better spend on SSKs and MPAs.
The IN's opertion of a carrier for the past 50 years has always been for operational reasons. You are ignoring how things work out during war, when you simply look at numbers. Naval warfare is not simply about destroying each other's ships, but also about protecting our sea lanes. Also, the days of naval armadas facing each other and shelling each other to attrition is over - that is not how future naval battles will look like. It won't be like the tank battles of WW2, where N1 ships face N2 ships face to face, and N1 wins if N1>N2.
It is all about selecting targets and attacking them sneakily. Remember, ships travel at about the same speed as a car on an Indian road, if not slower. Their battle groups won't oblige us by floating upto ours for a grand battle. Here is a likely scenario:
Suppose a convoy of Indian ships are bringing in material required for our war effort (fuel, ammo etc). Or it is simply a convoy of Indian merchent ships, vital to our trade. And we realize that a pakistani naval flotilla is heading towards them to attack them, and the they are only two hours away. Our naval ships are at least 8 hours away. How do we protect our ships?
Supersonic jets from the vik will take off, decimate the pak fleet and return before they can engage our ships, even though our CBG is 8 hours away. Our convoy reaches home safely.
One squadron of 4.5 gen fighters in the middle of the arabian sea gives us a much larger radius of invincibility than ships alone can. Ships travel at 35 mile an hour. The power of a navy is in reach - with an a/c, the reach of the navy is far greater than without. How far we can attack or protect, how quickly we can attack or respond etc.
About land strikes - yes, the IAF will be in a better position to do that. But in the last war we fought, the navy struck many targets on land in b'desh, even though the targets were much closer to our mainland than west pakistan is. Surely that was not because the navy wanted some limelight?
I havent even begun to scratch the surface on how an a/c benefits the navy. Next consider surveillance and target aquisition. How much surface area of the ocean can a few migs flying high scan, and find targets to attack, as opposed to a surface platform?