There are a ton of theories on this but the general rule is 1 set (plus warmup) is for POWER, multiple sets is for "Development" and muscular endurance. The 1 set technique is pretty commonly used by traditional power lifters. I did this type of training exclusively for a year, developed tremendous strength but also experienced more frequent injury related to lifting. This could be attributed to the heavier weights being used to achieve failure (exhaustion) or it could have been attributed to underdeveloped connective tissue due to rapid strength increase, etc. Who knows.
I hesitate to recommend straying too far from the standard 3-sets 8-12 reps program. It works very well for MOST.