Why can't the ACs run off propane too?

After reading the con's of generators and the pro's of solar panels, it seems that most of us would prefer not using a generator. However, as some folks pointed out, summer camping in many areas is unbearable without air-conditioning - which seems to be the main reason for the generators. Since the refrigerator can run on 120 volt, 12 volt and propane - why can't they design an AC unit that works the same way? Refrigeration cycles are the same, whether AC or refer, and the air mover can work with 12 or 120 volts, so where is the problem.

I can only imagine the problem is how large it would have to be but if someone knows, I'd be interested in finding out.

Thanks,

Mike