Re: Who cares
Since 1970 they have been very much like battleships - huge lumbering targets with very little effective power in any *real* war.
It is entirely possible that you are right, but impossible to know, as such a scenario has not occurred, and so never been tested.
Who's to say that saturation missile attacks work? There's as much reason to imagine the missiles might screw up, and mess with each others flight/targetting) as there is that the defences will.
After all, modern anti-aircraft destroyers are theoretically capable of shooting down 2 or 3 missiles a second, out to long distances, until they run out of ammo. In the case of the AEGIS system in the US, the different ships can even pool their missiles, so as not to all engage the same targets. So a carrier battle group with a couple of anti-air cruisers and some Arleigh Burke destroyers has well over 500 missiles to use - plus the short range SAMs on the frigates and everyone's gattling guns.
Now admittedly if a carrier gets into fighter range of any major power, you'd expect its air group to be overwhelmed by sheer numbers. But far out to sea, where only long range bombers can reach (un-escorted) a carrier is a much more formidable target. The further away you launch your missles from, the less targetting information they'll have, and the easier they'll be to avoid/jam/spoof. The closwer you launch, the more likely you won't get to. If you launch from far out, the air group may also get to shoot some missiles down, before they get into range of the SAMs.
Also, the Russians don't have the vast regiments of naval aviation they used to have. I very much doubt they can field 150 long range naval bombers anymore - so the attacks would be less saturating. Obvously China still does have the numbers. Taking carriers into the Taiwanese straits would almost certainly be suicide. But carrying out a distant naval blockade of China and attempting to escort resupply to Taiwan might be possible. Assuming there are any plans to defend Taiwan, but it's the most likely large scale conflict that comes to mind.
Also, you don't just have to deploy one carrier at a time. A fleet containing say 4 Nimitz class ships has an airgroup larger than the airforces of all but the top 10 global military powers. They could field 5 or 6 squadrons of F18s each, plus tanker, ASW and AWACS support.
Obviously the RN are much smaller - ours would only be a component of a larger allied force if fighting a first rate power.
Carriers were never really designed for fighting land-based air power. And mostly avoided it even in their heyday in WWII. Purely because of the numbers issue, although of course they got into fights against isolated island-based airgroups. Now that global air forces are much smaller, that's probably less of an issue now than it was back then.
Finally carriers also have many uses. Getting air power to places where it's needed. Quickly. You don't have to waste time negotiating for air basing rights, when you can just float into position. You can also use them for disaster recovery, the US Navy did an awful lot of work after the Boxing Day tsunami for example. And also protecting your sea lanes. From both air and submarine threats. If you're a country with a large trading economy that's rather vital. Plus supporting troop deployments in places from the Falklands to Afghanistan, via Sierre Leone.