On the perceived tactical disadvantage of a cross-draw rig’s position, well, the very same default “flinch” position, that protects the left side of my face and torso from an incoming strike, as I pivot my right leg to the rear, places my left forearm and elbow in a favorable position to not only shield the cross-draw rig and handgun, but, to come down HARD on an opponent’s arm/hand, if he reaches for my holstered weapon.
One prominent argument is that a cross-draw rig is a farther reach, for the weapon hand, if it become necessary to draw. Well, if my hands are at mid-centerline, at or lower than the height of my sternal notch, my weapon hand is actually quite near the grip of a weapon that is carried cross-draw. Personally, I rarely stand, in public, with my hands hanging limp, at my sides. I tend to bring my hands together, at my centerline.
Then, there is the “thoughtful” position, with my left hand at my chin, as of posing for a portrait, while wanting to look thoughtful. It is perfectly normal-looking, to then have the right hand positioned by my left elbow. Jack Benny was known for assuming this pose, during his comedy/acting, and should be readily search-able, on-line. Notably, his hand is normally on his bicep, but we modify this, so that the weapon hand is under the opposite arm’s elbow. Now, where is that right hand, in relation to the cross-draw holster? NEAR the weapon. It can even be ON the weapon, while the weapon remains hidden, if the cover garment allows it.