Let's assume an aircraft carrier is as vulnerable as many people claim. An utterly false assumption, but for argument's sake, let's assume it is.
Suppose China or North Korea opt to sink or otherwise take out a CVN. Would that be an explicit and very visible act of war? I tend to think so. What would the US response be to such an action, even assuming the US decides not to use nukes as its response? Would whoever took out the CVN shortly be on the receiving end of a VERY devastating (non nuclear) response? I tend to think so. I also tend to think that whoever is contemplating such an action would think so too and upon further contemplation would be dissuaded from even attempting it.