The interesting thing about full-cheek snaffles is a lot of western riders use them too, for starting colts (ie. John Lyons). Western headstalls never have the bit keepers with them.
Now I see how the keepers hold the bit in a nice position from the photo posted in the beginning of this thread. So I am not going to say the keepers don't serve a good purpose. But I also don't see how not having them really hurts anything either. At the very least, it would function like a D-ring, as someone else said.
As for getting the bit stuck in the cinch or other tack- I've had that happen once too, but not with a full-cheek, with a curb! The horse reached around to bite an itch and the end of the shank went through his string cinch and got caught there. He started turning in circles kind of frantically, but luckily he's a level headed horse and after a moment stood still so I could jump off and get him unhooked. So that is a possibility, however remote, with other bits too, not just full-cheeks.
I am a western rider, but kind of look at a full-cheek as a snaffle with almost a side-pull function going on at the same time. So I think it's a very useful bit. It's a mild snaffle, but you can manually turn the horse if you have to too.