To kill a carrier in carrier battle group is tough job (though not impossible)
1. First point of defense is Patroling aircraft (su30mki/MiG29K)
2. second layer of defence is Air defense ships (usually frigates n subs) with 3 layer of security, LRSAM, MR-SAM, SR-SAM
3. 3rd layer of security is Carrier itself, the SAM on carrier
4. 4th layer of security is gatelling gun, it create a wall of bullets in front of invader...
Finally, if missile hit Carrier the massive size of carrier itself is defense , It will be unusable but not destroyed...
Welcome Carrier Killer....
You can't just dismiss a threat just like that.
The above is true for all carriers, not just yours.
The above factors make it more difficult, but it doesn't make it less of a threat.
What if for example, there are 2 enemy aircraft that ripple fire 4 ASM at you? Or more?
Rest assured, if an enemy wants to kill a carrier, they will do whatever they can to overwhelm the carriers defences.
1st layer of defence works if you intercept enemy aircraft in time, given that it can fire an ASM from well above 100km away, makes that more difficult.
As for SAMs, the Indian holds a gem of a SAM, the Barak 8, but AFAIk, the naval variant has some 70km and a flight ceiling less far less than the altitude the CM-400AKG will make in it's approach.
So yes, Barak 8 could successfully intercept one, maybe two or more. But somewhere along the line, there is slight probability that it fails, especially if you consider the fact that the ASM head towards you at hypersonic speeds. there it always a probability of failure to intercept. And the odds way heavily for the carrier, if the missile is intercepted, the enemy loses an ASM worth $ million or a few ASM worth a few million, if the ASM is not successfully intercepted, your $ billions carrier and it's on board aircraft are in danger.
Then you mentioned Gatling gun, or CIWS, these only work in certain areas around the ship and only as a last resort, they intercept it the missile from very close range, the probability of interception for a hypersonic missile at such close ranges is also a problem. And also, if CIWS successfully intercepts the missile approaching at high speeds, the debris of the missile still hurtling towards you at high speed poses a threat, one that the ship can't and wont attempt to intercept.
I'm not saying carriers wont shoot down ASM.
After all, they are billion dollar assets and people who own them, will make an effort to protect them and will protect them very effectively.
But don't just assume that they aren't a threat.