I would also be mildly concerned about smacking myself in the cheekbone with the slide.
Not surprisingly this was a concern for several people during the class. However, the truth is, while you are holding the gun closer to your face than you would in a more traditional stance, the reality is that you're still holding the gun more than 8-10 inches away from your face, so it's a non-issue.
Likewise, there's no getting a flash burn on your face; the gun is simply too far from your face.
Also, because of the mechanics of your arms and hands, there is basically no rearward component to the recoil impulse; just some muzzle flip which is also greatly reduced. or to be more precise, it's much easier to control muzzle flip in the CAR position.