My weak hand drill is deployment of a fixed blade knife from weak-side offset appendix. This can be deployed from the ground even while mounted by a determined training partner who is pounding away (with boxing gloves of course).
I'm not sure what practical usefulness there is in working the off-hand pocket draw technique. If there is distance between me and my attacker and my strong hand/arm is wounded then that is almost certainly from incoming. In this case if I don't have time to draw, I should be running for cover. The practicality seems very low and I have other training priorities which I consider to be much more important ie.: empty hands, clinch, grappling, and shooting on the move, to name a few.
If someone has jumped me and my strong side draw is fouled for whatever reason I would not go for a pocket pistol,
with either hand. The likelihood if this tactic being successful is very low. It's much more likely that I'd become fixated on the weapon while the other guy proceeds to carve me up or cave in my skull.
A j-frame carried AIWB? Now that's another story entirely.
I agree that pocket carry is weak for any scenario where you expect even the slightest possibility of being taken by surprise. If you are lucky enough to see a threat coming then it's not hard to "prep" your draw from a pocket, but trying to draw from the pocket mid-fight is a recipe for disaster. In my mind their exists only two legit reasons for pocket carry: deep concealment, and convenience. Don't get me wrong I pocket carry very often, but only because I carry everyday and nearly everywhere.