In modern naval warfare, no ship is immune to an air attack whether it is by a manned aircraft, a missile, or a drone, and the larger the vessel, the greater a target it would be; agility and low profile are the new norms. Consider what the reaction in the US would be if NK, Iran, or even terrorists were to lob a few well-aimed missiles or drones at a US carrier and sink it...
For an example, look back at the Falklands War and what happened to the ARA General Belgrano...
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