The other problem is that the enemy has to
know where the CVN is, and the surrounding battlegroup to actually hit it. Even if it's a matter of, F-it, the balloon has gone up, it's full on WWIII lets launch ballistic nukes at it!
Perhaps this seems silly to say, but it's a big ocean. And unless sub, aircraft, or satellite has a position on the carrier group, and keeps it updated, even the biggest nukes, or a Hail-Mary spread of MIRV's could be nothing more to that CVN than some glow on the horizon. And presumably, the battle group will be scanning aggressively for aircraft and subs. Probably doing a few things that aren't done in peacetime, even in the most stringent of exercises.
And as to satellites, they don't turn on a dime, fuel is limited, and when one is diverted, it's something like another 90 minutes before it can fly over it's target again. At which point, the CVN could be as much as 45-55 miles "somewhere else" within a circle with a diameter of 90-110 miles. That may not be an insurmountable issue for an airstrike and anti-shipping missiles (not counting the battle group and air cover), but is likely to be a problem for an ICBM/IRBM.
And considering that an Aegis shot down a re-entering satellite as an exercise, granted one that was known to be re-entering, and planned months beforehand. I still have to wonder what our
undeclared abilities are in regards to Space War, and God knows what else, when failing to use those no-such-assets is more costly than not using them.
ETA: Rev made the exact same point 1 minute ahead of me.