What Happens if a Navy Aircraft Carrier Is Sunk?

One of two things: either the US is going to reach down and find their collective testicular fortitude and come out swinging OR the apathetic public will be "woke" and insist we capitulate and send the enemy emissaries home with an apology and a warm cookie.

From a technology stand point, we may not be able to move fast enough with a capability counter measure, or our counter measure will be short lived with a counter to the counter. This Science and engineering race goes while combat operations continue, impacting Force employment operations

A carrier is too tempting a target to not assume that every (real, nascent, potential) enemy dreams of sinking one. Can it be done? Sure. Will it be done? Maybe. Should we stop building and deploying them? Hell no. Nothing allows the US to project force like a carrier. It's an important element in defense and peace keeping. It also allows the US to respond to distant disasters with transportation capabilities, medical services, electrical generation, and many other services that are critical in such cases. So, when you look at the cost/benefit ratios, they are worth the risk. And when you measure the probabilities, remember that a carrier is always surrounded by other assets, linked in command and control, functioning as a unit, and that other "cheaper" assets will throw themselves into the path of any weapon that eludes the protective umbrella of electronics, planes, missiles, and guns that protect every carrier.

Yes, a aircraft carrier can be sunk. No one has ever built the perfect anything. Especially so if one must rely on technical marvels to overcome a mostly P.C. crew. Entropy never fails.