If you wet brine a piece of meat and don't apply anything else to it, why exactly do you need a bag?
Why not cook the meat directly in the brine? While it cooks, it can brine some more. Handy, if you are short a couple hours on the brine.
I always thought, that the point of the bag is to keep the meat dry. But when you take it out its swimming in a lot of liquid.
So why not simply cook it in water, still controlling the temperature precisely?