Ummm because for the run of the mill 60m / 35min dive you can dive your 10/70 dil or whatever you like and bail 18/45? (or get switched to)10/70 hypoxic. I'm not happy to breathe that on the surface for any length of time and even take precautions not to inhale it through the ADV until I'm on my way down.
I'm not changing the way I dive to suit whatever diluent I happen to have. It caters for what I COULD have.
Does it matter where the BOV is plugged into? If it's offboard, it's still the same/similar gas unless you add the clusterf*ck of gas blocks and switching.
The gag strap is more to stop you inspiring water and drowning rather than worrying about wtf you're breathing.
As I said, the mask strap goes under my hood.
None of this is a perfect solution but what I do works for me and the gag strap adds a massive level of comfort to my everyday diving regardless of the miniscule possibility that it would prevent me from drowning.
For the vast majority of CCR dives without support divers (so say those in the ~75m range) your rescuers can put you onto a breathable gas.I don't see how any of this scenario is different if you have a BOV in your mouth, aside from adding even more complexity for your potential rescuer(s). Unless I'm missing something?
EDIT: I almost always dive alone, so this is all a bit academic really
Doing 100m+ 10/70 dives solo, no buddies, no support... welp good luck with that in the long term. Te gag strap is just window dressing here.