That we ended up with compressor refrigerators getting the lion's share of benefit of mass production is a tragic accident of history: General Electric drove refrigeration into homes, and wanted to build electric motors.
Interestingly, Albert Einstein and Leo Szilard made a foray into the field, patenting an electromagnetic refrigerator that was not commercially successful.
https://invention.si.edu/einstein-szilard-refrigerator
Update: from a quick look at the patent referenced here, it seems to be a rather conventional heat-driven absorption refrigerator - the plot thickens!
Update 2: The above article is conflating two different inventions. Einstein and Szilard also patented a compression refrigerator driven by a magneto-hydrodynamic pump of their invention, which used an internal liquid metal as its moving part and consequently required no seals to keep the refrigerant from leaking. It was far from being silent, however.
http://www.physics.smu.edu/scalise/P3374fa16/EinsteinSzilard...
They are far less efficient than compressor refrigerators.
If you're willing to deal with a chest-fridge built from a freezer it might be acceptable power consumption.
Edit: Watched the freezer video. Performance is predictably bad, but not as awful as one would expect. Might actually be a viable daily driver with thick enough insulation or vacuum panels.