Fwiw, I believe part of the reason to use this position is for in case the first person you encounter going in the door is a hostage (e.g. being used as a shield), or simply someone standing there unarmed and/or where lethal force is not justified. One can then simply pull the person aside or down with the weak arm.
If the unarmed person attacks you (and lethal force is still not justified), you can give him an elbow strike, followed by more strikes, or a takedown move, while retaining your pistol further away from his gun takeaway range.
If lethal force is later justified, one can fire from the retention position for close encounters or transition to the two hand hold for more precision or more distant shots.
As to who teaches the method, Mr. Humphries' GSGI school does, for one...