Some good points raised here, but some of them would be more plausible if the correct terminology was used:
Ice forming around the condenser in a fan assisted fridge
The part of a domestic refrigerator that can get iced up is the
evaporator.
how quickly the compressor exchanges heat is the main factor in efficiency
The compressor does not "exchange heat". It is merely the "pump" that circulates the refrigerant around the system. The
condenser is the heat exchanger. The efficiency depends on many things, one of which is the compressor.
The compressor being enclosed can add to expense as fans are sometimes needed to aid cooling
If fans are used to assist cooling they will be used to help cool the
condenser, not the compressor. The condenser is where the heat is released, the compressor suction is pulling cold vapour from the evaporator inside the cabinet, and gets most of its cooling from there.
Many commercial fridges have the compressor at the top which makes more sense as heat rises
.
The complete "condensing unit", ie; the compressor and condenser, usually with a fan, is mounted on the top more for convenience and service, rather than energy efficiency.
Does this mean that the older models, which have all the pipes visible at the back and the compressor open at the bottom, are more efficient / economical than the all enclosed flush -back newer models
No, it doesn't.