Squirrel,
Including Somalia I can think of support in a couple of other NEOs and one other use that the Harrier was the only player.
There are multiple reasons against CVN use. When TacAir integration was started Marines would show up (for boat squadron duty) and have CAS training relegated to low priority. Currently there is more "CAS" training for all I'd caveat that to be dropping ordnance in close proximity to friendly forces under current circumstances.
The training priority for the CVN/CAG is OCA/DCA for obvious reasons. How much are going to get for training (initial, currency, and proficiency) to include additional personnel to turn wrenches?
The "C" in of itself is a more capable airplane in all areas once airborne. It has it's own additional costs though; the larger CVN and battle group, further back from shore so ready five alerts are further away in time when the grunt needs help, tanking from land may not help and brings it's own set of political problems. When you have 4-12 men in a third world country which is your preferred option for support 1) B in 5-10 minutes or 2) C in 20-30?
The other practical point of a CVN versus a gator is that everyone watches the CVN and where they are parked while not paying attention to the gators. The lack of media attention and thus political pressure has allowed fixed wing usage.
I'd be the last to argue that the USMC should get B before the C. I am going to wade into assuming knowledge of the British situation but my quick take is that a CV(N) a little larger than the French with F-35C seems to make more sense.
In the end I think it will be political advantage over cost/capability, similar to the tanker replacement for the USAF; Democrat = Boeing (unions + overseas support of China), and Republican = Airbus (non-union + France has been helping on GWOT outside of Iraq and lots of help other places).
S/F, FOG