True story, the majority of missiles used in naval combat have been successfully defeated by countermeasures alone without resort to point defense weapons.
Inertial nav would be useless against a moving target. It can hit a fixed point in space within a certain CEP that is fairly large, but it cannot hit a moving target reliably. JDAM II has to use a semi-active laser to hit moving targets. INS and GPS are insufficient.
Mid course guidance implies something up in the air guiding the missile to the target. Such a vehicle will have to fight it's way inside the carriers air cover. Good luck. It's guidance signal or data link is vulnerable to jamming, just as it is with a cruise missile that requires mid course guidance.
This missile warhead will need some sort of active homing or a passive IR or IIR seeker, and that puts some limits on it's speed, and on how close the seeker must be to find the target. On re-entry through the atmosphere it will be blind and out of communication, so it will have to wait until it has re-entered and cooled before it can use any sort of data link or on board guidance to find and target ships.
This is not a trivial engineering problem.
And, somehow, Admiral Lyons managed to sneak the Eisenhower battle group right up to the Kola Peninsula without the Soviets detecting them, and we also put carriers in the Sea of Okhotsk without being detected. That last one was back in 1989 and I remember it well. You underestimate the ability to hide naval units with tactical deception.
I all to clearly remember how hard it was one hazy day to find the Nimitz at sea, and they were helping us find her so we could land. A carrier is an awfully small thing in a vast ocean. Go to sea, lad, and see what I mean. Have you sailed the South China Sea? I have and it's a darn busy place with lots of ships and weather to hide among.