I wouldn't call absorption-cycle deprecated. In fact, I would definitely by an absorption-cycle fridge if it was available in similar size as my current fridge.
Absorption-cycle fridges can be made practically silent while the ones with compressors are very noisy (maybe not the top-of-the-line, very expensive ones but still). I have my fridge in the living room so it would be worth some premium for me to have a completely silent fridge.
Moreover, I have a huge solar-hot-water-collector array, which over-produces in the summer so I would run that fridge for free (if it had external input option)
Unfortunately, nowadays, only very small fridges can be purchased with absorption-cycle. These are designed for RVs and only have propane input.