You'll find the trend in the armed forces to be towards multirole capability and greater longevity across the fleet: reflecting the realities of modern defense procurement, maintenance systems, and keeping value in the operated airframes. In the 1960s it wasn't uncommon to have a dozen aircraft types operating in very specific niches (A-1 Skyraiders, A-4 Skyhawks, A-7 Corsairs, A-6 Intruders were all contemporary. There were F-102 Delta Daggers, F-106 Delta Darts, F-104 Starfighters, and F-101 Voodoo in the same period as well). As the military industrial complex has shrunk, program costs have also gone up, and the weight of numbers that made dozens of different aircraft types viable (one company would make one aircraft then go on to the next iteration, and so on and so on).
So when we look at the C-2 Greyhound, and its predecessor the C-1 Trader, the idea was that no other airframe could take off with large cargo and fly it to a supercarrier well away from its base, and having a carrier go into port in the middle of a war was a huge waste of time in a war decided by hours (as you see in your well-researched CMANO scenarios). It makes a lot of sense then in the modern procurement scheme to make this more flexible, not less: and in an era where specialized airframes are going by the dodo (S-3 Viking, EA-6B Prowler, E/F-111, etc.) the more versatile system wins out.
The CMV-22 is an off-the-shelf product. Its production line is in place, the costs are known, and the value is already demonstrated. That is huge in procurement. More importantly, it has capabilities the Greyhound and Helicopters don't. Much further range, roughly equivalent cargo capacity in a larger volume, low stress from airframe hours (if you don't have to whack into a carrier at recovery speeds, you really shouldn't. So bad for the plane.), and most importantly the ability to recover supplies and bring them to the boat from anywhere.
Look at some of the scenarios you've made: in Longest Battle, the CMV-22 can resupply any ship at range, not just the Kennedy. It can drop off missiles, spare parts, personnel and more. In Hold The Line and Changing of the Guard, CMV-22s operating from Enterprise could be actively resupplying her from range, going to-and-from the supply ship at hundreds of NMI range. It could land at Goose Bay, where C-17s and C-5s could be unloading ammo stocks and handling the long-range transit. If battle damaged, those ships can still recover CMVs, and the CMVs can medivac wounded from any vessel in the fleet. Lost pilots can be CSAR'd well away from helo range.
Is it perfect? No. It can't be pressurized, it's big, it's likely a maintenance hog, and VTOL training pipelines are very complex. Yet it can do a job other aircraft cannot, in a way that is very multifunctional. It wouldn't be a bad recovery tanker, either, especially in the nightmare scenario: bad weather, pitching deck, low fuel on the recovering aircraft. Putting down a VTOL on a big carrier deck is easier than landing a fighter.