... I'm not against a class, but rather the methods taught. As shown in that "Briefcase" clip, the free hand is more than likely required to push aside a gun in your face. While doing this, the gun hand draws and fires.
Which is exactly what is taught at classes focusing on close-quarters defense or portions of some other classes. I think perhaps what is happening is an inaccurate assumption on your part: that the techniques you've disparaged represent the whole of what is taught
. That's simply not the case. I am unaware of any school teaching a full-extension draw for close-quarters engagements.