Producing and storing small dedicated quantities of electricity is hideously expensive. Tiny amounts are not nearly as costly as "small amounts". Thus operating an absorbsion refrigerator is not nearly as pricey as operating it on alternating current.
Permit me to throw something into the arena here.
Take the alternating current motor and chuck it out the kitchen window. Replace it with a direct current motor. I'll have fun here and let another participant do the energy calculation between 12-volt battery direct motive force and battery to AC energy translation.
What is missing is availability of DC motor/compressors. My 18 CF Vestfrost freezer keeps food throughout at -5F on a 100F day for 47 Ampere hours for 24 hours. Double this figure for 12 volts rather than 24 volts. Ninety four amp hours per day. All freezer. 18 cubic ft storage. On a blistering day ice cubes snap and pop when cold soda is poured over them. Rock solid ice cream on the front of the shelf next to the door. Frequent door opening, rapid temp recovery.
So lack of DC motor/compressor availability is the handicap. Inverter conversion is awful. So is AC motor energy waste. I haven't perused information for DC compressors. It would take Chinese or Indian manufacturing cost efficiency to make the dream accessible.
When I saw a stupid stupid Snap-On 12 volt test light for sale yesterday for a hundred dollars, I knew then the die has been cast forever.