11. Are there situations where compressor-based systems make more sense?
Yes. Generally, whenever a small compressor-based system would clearly be 'overkill' in providing a cooling solution, TE systems become the most viable choice. You find a 'gray area' amidst the medium-sized cooling jobs; here decisions ultimately come down to critical cost/benefit or design engineering considerations which are unique to each application. Given the present state of technology—unless there are unique overriding concerns—the compressor-based approach has distinct advantages in larger cooling systems such as standard-sized refrigerators and air-conditioning systems for buildings & vehicles. However, ongoing research into materials may one day make thermoelectrics practical for many of these larger applications.
This is from one of the manufacturers of Peltier effect devices. Source: Tellurex Corp.. Now, what do you suppose these kids know that Tellurex Corp doesn't?
They each got $25k college scholarships?