Then again, when you switch shoulders shooting, you don't switch hands, you still keep your primary hand on the pistol grip and secondary on a front grip or handguard. You just shift the rifle left (or right) into your weak shoulder (best practice, you are still best at shooting with your primary grip). This does mean that you hold the rifle closer to the centre of your chest and don't fully rest your cheek on the cheek rest of the rifle as per normal. Instead your head is slightly elevated over the rifle, possibly looking through a secondary close range optic.
This makes that less of a problem. Although extraction gases in my nose and the albeit slimmer chance of having my teeth smashed in would not appeal to me.
Also brass holders help with you and the rest of your section not all fall over slipping over spent cases on flat, hard concrete. That would be a way to lose a firefight.
And yes it is also possible to use a brass catcher to ensure that your teeth don't get smashed in a secondary
re-purpose. But I suppose just mounting a three-sided rectangular bracket (open side facing forward) over the ejection port will be enough to ensure no casing come backwards. A much simpler, cheaper and practical solution-I wouldn't want to carry a bulky, dangling, noisy sack of war confetti with me.