There are many reasons but most prominent are environmental ecology and reliability. CFCs are a major player in the depletion of the ozone layer. In addition, CFC's are nasty greenhouse gasses. While the recent HFC and HCFC replacements are less harmful, they will still be major contributors to the greenhouse effect and there is concern over possible health hazards for many of the newer chemicals. In addition, since both HFCs and HCFCs are expected to be banned early in the 21st century, an entirely new refrigeration technology needs to be developed.
Thermoacoustic refrigerators utilize no environmentally hazardous gasses.
And, because they can utilize waste heat as an energy source, they are extremely environmentally friendly. In addition, since thermoacoustic refrigerators do not use the compressors, lubricants, sliding seals, and other gizmos present in vapor compression refrigerators, the thermoacoustic refrigerator should be more reliable. Finally, since thermoacoustic systems tend to work at higher frequencies and at single frequencies, noise and vibration control is actually easier than for a conventional refrigerator - so thermoacoustic refrigerators should be even quieter than the refrigerators of today. The new thermoacoustic-Stirling cycle heat engine developed at Los Alamos is a fantastic breakthrough. It provides high efficency basis for the conversion of heat to mechanical power without moving parts.