The 1-arm crawl you describe was a drill we used in our earliest swim camps, in 1989-90. I included it because I was familiar with it from my days as a coach of competitive swimmers 1972-88.
While coaching competitively and at those early camps, I taught that drill with considerable rigor and close attention to form and feeling. In fact I had swimmers compare their Swim Golf scores (strokes + seconds) for 25y/m of right arm vs. left.
We dropped that drill in the early 90s because it no longer matched our evolving technique priorities. In fact, it directly violated them.
Ever since the early 90s we've been guided by the dictum that "The shape of the vessel matters more than the size of the engine." In other words, reducing drag matters more than increasing propulsive power.
The single-arm drill in which you leave one arm forward has three significant problems
1. The swimmer focuses on pushing water back with the arm.
2. By starting the push-back in a flat-on-the breast position, there is no opportunity to use weight shift as the source of power. Instead you rely wholly on fatigue-prone arm and shoulder muscles.
3. It emphasizes and relies on steady flutter kicking. It can easily become a kicking exercise.
Any drill you choose to do should observe and promote the same principles as the whole-stroke you are seeking to develop.
In our case that means
1. Use available forces (gravity, buoyancy and body mass) to generate power before using muscular forces. In freestyle and backstroke, this occurs through weight shift. There is no weight shift in the drill you're doing.
2. Use powerful and fatigue-resistant larger muscle groups--particularly the core--before smaller and fatigue-prone muscles, like the arm and shoulder.
3. In the case of the Catch-and-Press (which this drill claims to develop), focus on Holding Your Place rather than on Pushing Water Back. This drill does the opposite.
Our 2.0 Freestyle Mastery Self Coaching Course http://www.totalimmersion.net/store/...aching-courses
includes a Single SIDE drill (as opposed to Single ARM). It observes and promotes the three technique principles I list above.
You do it with the non-stroking arm at your side (hand in 'Cargo Pocket' as in our Torpedo drill). You use weight-shift/body rotation to propel past your Catch. You use arm/shoulder muscles to Hold Your Place.