one of the big reasons for appendix carry is -
it's supposed to be possible to draw when a bad guy has you in a bear hug or pinned with the arms trapped. The theory is, if your hands can still wiggle around- you should be able to draw the gun- and make a Hail Mary pelvic shot on the adversary.
I think that for a complete self-defense training regimen you should train enough grappling to be able to get free of the bear hug. I wouldn't want to be drawing a gun when I don't have a whole lot of control over where my arms go.