The only downside to the residential fridge operating on invertor is the weight factor of the fridge/additional batteries/invertor and those solar panels but to get a fridge that would handle the summer heat for a fulltimer it would certainly be worth the sacrifice of leaving something else off the packing/carry list to compensate.
For those of us who don't boondock at all, that approach might make a lot of sense. If you were to find yourself without park power or "stuck" some where for a time you could always fire up the genny and recharge batteries as well as run the fridge for awhile to maintain. The trailer going in for a service call could be handled by insisting that the service facility provide a minimum of 20 amp continuous service to trailer while they replace the air conditioner for the third time.
Sorry, I couldn't help myself!