Even the Alternate Command Center within the Cheyenne Mountain Complex can be destroyed by an enemy nuclear strike. That doesn't mean it should be done away with.
The U.S. has used big carriers many times since WWII to our advantage. And as long as we have the right mix of nuclear and conventional weapons - and a tough Republican president - our big carriers are probably safe.
If a Democrat is elected president, all bets are off.
I expect that the bulk of the carrier force will be held in reserve until the “Big Blow-off” occurs. Once the SSN’s & Stealth Fighters sanitize the sea areas and the tactical nuke exchange happens, or does not happen, then the CVN’s will move out in multi-carrier CVBG’s. Those will provide the bulk of the strike aircraft in-theater.
Even in WW2, the old pre-war dreadnoughts had a role to play. The fast battleships pretty much lacked for targets, but they were massive AAA batteries for protecting the carriers and pretty much couldn’t be destroyed by Kamikaze attacks for even multiple heavy torpedo hits (had the enemy been able to get those on target).
So yes, the CVN will have a role in a major war, albeit a secondary follow-on role. But in any war short of that they have tons of utility.