Try as I might, I can't find the previous thread where there was a picture of one of these. Someone mentioned having found them in a facility where 120VDC equipment was manufactured. They were used for testing DC equipment, I guess.
I'd say you would have used these anywhere the voltage or frequency differed, or where for some other reason you didn't want people plugging in standard stuff.
I gather the NEMA configurations were developed in the '60s; people on ECN have said as much. Nowadays, there is a configuration for every AC voltage and class of service, but you might still have a special purpose. For example, in off-grid solar-powered homes, it is common to run low-power DC loads (cordless phone, answering machine, alarm) directly off the battery, to eliminate inverter losses. The usual practice is to use a 6-20R for 12VDC loads. Many AHJs will accept this if there are no 240V circuits in the house. 406.3(F) requires that receptacles connected to different voltages, frequency, AC or DC, be of non-interchangeable design, but does not specify anything further.