Fridges use very little compressors, condensers, & evaporators since the air barely circulates and is in a sealed box. Often the circulation inside the fridge is simply convection currents of hot cold air rising & falling. No fan inside at all.

As you increase the size of the box, i.e. Fridge, car, house, store, stadium, more air has to circulate to cool the area.

Small compressors & evaporators will not effectively cool air fast enough to be force blown across the evaporator and through the "box", so the sizing has to increase.

Combine that with the lack of insulation / greenhouse effect of glass windows in cars the size required to cool an area increases.

I believe that an electric AC unit in a car would work. It could be driven by electricity from an alternator and be more efficient BUT it would cost more to produce because while there would be a decrease in AC component costs it would require a sizable increase in electrical capacity and some modifications to the charge system to power the unit at idle. Car companies go for cheap.

I had toyed with the idea of using peltier coolers on a water cooled plate but got sidetracked. It could be a fully contained electric cooler (like they use in micro electric fridges) but I'm sure if it was feasible it would already be done by somebody smarter than I.

Yours is a good idea though, a compressor from a small window unit AC might be the best choice over fridge unit.