Arthur Jones was right after all! May he rest in peace.
One set per exercise will definitely work, because if one hard set didn't do anything, how could more than one set?
The key issue is balancing intensity of effort against overall volume. If you're only doing one set, it has to be a pretty dang hard set to stimulate adaptations. This forces you to train close to your limit, which is not always a good thing. Also, this style of training can require real psychological effort -- and not everyone can sustain that for long periods of time.
If you use more volume, you can balance that out with less intensity. For example, doing lots of singles with 70% is not really "hard," but is a very valid method of getting stronger. On the downside, doing a lot of submax volume requires a larger time commitment, and usually requires reducing the number of total exercises in your program. Some people don't like that.
The most productive training is high intensity and high volume, but that's not sustainable over the long term.
For "the average person" with average goals, single set training could definitely meet their needs. But so will any other non-stupid lifting program.
As an aside, I've thought classic HIT-style workouts (like the early Nautilus bulletins) would actually fit into the CrossFit framework. I know, heresy.
"The enlightened never cease forging themselves."
-- Morihei Ueshiba