I'm a bit confused. Riding with cages and no straps basically ignores the Orange, Blue and Yellow phases in the above diagram. If you were actually applying 'positive' force with that foot in that particular part of the pedal stroke, you'd be coming out of the cage. Otherwise, isn't your upward moving foot (while in that range) actually applying a force of resistance against he opposing downward foot in an effort to maintain it's attachment to the pedal/cage???

I don't doubt that training this way changes your pedal stroke drastically and takes time and patience...but I don't see how this is teaching circular pedaling.

It's the reason that true 'spinners' hate riding bikes with only platform pedals. It's almost dangerous to do. Immediately, the spinning cyclist is going to have his upward moving foot lift off of the pedal because he's trying to apply the positive circular force to that pedal, while not being attached. This is why one-foot drills (while clipped in, and on a freewheel specifically) alert you immediately to the 'dead spots' in your stroke because you'll be releasing the positive force and will feel/hear the drive-train re-engage when you finally reach the 'power' portion of the stroke. With practice and muscle development, you'll be able to keep constant forward circular pressure on your pedals for some time with no breaks in power delivery.

-Jeremy