I am only going to present this, not because I am an expert or part of SWAT, but for the sake of discussion and because I also learn from constructive criticism.
First of all, the reason why I think this technique is not widespread is because ballistic shields are preferred. Also, this technique address a very specific issue: Dynamic entry for point in anticipation for close encounters (with the absence of shields).
My take on it is that you have a perfectly good offhand and you can either use it or lose it. The whole idea of the offhand in a guard position (aside from what s_lew has already mentioned) is so it can parry whatever weapon we encounter during entry just long enough to squeeze off a shot. My hand usually floats about one foot in front, between my ears and shoulder, using the length of my forearm as a makeshift shield. From there, I usually either hook with my offhand, or just push. Both techniques are used away from my pistol's line of sight.
Several tools can be used in conjunction with this technique. The police Tonfa for example. Maglights can also work by holding it shoulder level just above your pistol. The most controversial tool is a knife in reverse grip.
Once you enter the room and if there is an enemy that is farther than the technique requires, I often find it easier to just punch my pistol hand out prior to squeezing a shot, rather than to waste additional movements trying to tap my body with my offhand before punching out with two hands. KISS.