I don't think this would really work out all that well, just at a practical level. Firearms really want to be just as simple and reliable as they can be, which is the downside of most so-called smart gun designs. If it gets to the point that you
have to pull the trigger, you don't want any doubt about whether you'll effectively have lead going down range.
The camera, storage, and power source would also need to be rugged enough to stand up to the stress and impact of repeated firings, and you'd have to keep that power source juiced up. I imagine you'd see a lot of dead batteries in gun-cams.