Comment by nerdsniper

As you stated, there would be no need to sink the carrier to remove it from service. Heck you don't even have to damage the carrier at all if you damage enough of its fleet. Sufficient damage to the tarmac of the carrier, the bridge, radars, weapon systems, and communications of a sufficient portion of the ships of the carrier group would remove it from service, for a very long time, especially if American/Korean/Japanese ports and dry-docks were also damaged by container ships already docked in/near those facilities (likely too close for our current missile defense systems to defend against).

Missiles are also an option, though carrier groups have some ability to defend themselves against them (less capability against hypersonic missiles, of course). The Chinese container ships are reported to have up to 60 vertical launch systems, which may be insufficient to overwhelm a carrier group and remove the carrier from service. It's reported that carrier groups can defend against "dozens to 100+" missiles.

That's why I'd imagine that it might be easier for a single container ship to disable a carrier group using 10,000+ drones instead of 60+ missiles. Especially as you wouldn't need fiber-optic cables, against ships a COTS AI targeting system would be sufficient (still robust against jamming, but allows for longer range than fiber-optics would).