Hi BFL13,
Actually I could run my air conditioner on a tiny generator--but I would insist on electric start--and no one makes one.
There are folks who do have enough solar to run a single roof top air conditioner--but admittedly they are a small minority. I could have been one of those folks if I had chosen more efficient panels--but they would not have had the shade and heat tolerance of my existing panels. For me it was a "better fit" to have a maintenance and extended boondocking solar system.
If I don't run the inverter much, the limitation for me is waste water tank size. For some reason the original owner special ordered a second fresh water tank--so I have water that I literally can't use--no place for the waste.
Unlike you, I believe a case can be made for paying for a solar system with savings on fuel from running a generator. That will only get better over time as fuel prices spike higher each year.