I do find it interesting to note that with all this talk about the vulnerability and by some the obsolecense of the modern carrier, a historical review really shows that the last time there was a real peer-to-peer shooting war with a US carrier was perhaps 1945 off Okinawa. Yes I fully understand there were other threats and actual attacks, but not a real a real death match attack from missiles, aircraft, submarines, or other ships from a peer threat. The Falklands for a few months in 1982 was another venue where carriers were actually targetted in a shooting war.
So while the modern carrier (or battle group) has been equipped to fight and defend itself in a major peer threat environement- this thankfully has never been tested. The overwhelming use of the carrier has been to provide power projection in peacetime and limited wars. I do understand that the math might change in a major conflict, but history has shown how they have been used and they seem to be quite useful for the few nations that can make the investment. I would not write off the carrier yet.