But we absolutely should have this. Ideally a police-issue firearm which had it milled right into the chassis.
Making room for the camera by removing a few bullets would help reduce the numbers of innocent bystanders who are shot.
Being less accurate would be pretty scary. http://www.popehat.com/2013/12/05/nypd-baby-you-know-we-love...
> As long as you ignore the fact that the shooting victims were innocent bystanders, hitting two people with three shots represents unusual excellence in marksmanship for the NYPD, matching another recent incident in which skilled NYPD officers were able to hit their target and nine bystanders with only 16 bullets. Overall the NYPD usually requires about 331 rounds to hit 54 targets, of which 14 will be innocent bystanders, 24 will be dogs, and 16 will be people the NYPD was actually aiming at. Statistically, if you aren't a dog, it is slightly more dangerous to be the person the NYPD was shooting at than a bystander (16 people out of 331 shots for intended targets for a 4.8% hit rate vs. 14 people out of 331 shots for bystanders, a 4.2% hit rate.) NYPD has a better success rate for other weapons, and certain factors, like shooting unarmed people in the back, tend to increase hit rates.
Perhaps it would (assuming that the timing meant that it was able to capture more than the flash of the bullet) in certain situations, but I think that the shoulder-mounted cameras that are always-on provide far more consistent value in protecting all parties involved to merit serious consideration of trigger cameras.
For example, here's one of the add-on modules Taser makes for this: http://www.taser.com/products/on-officer-video/taser-cam-hd
Outside of action movies, though, I doubt many officers shoot people or other targets that they are not looking at, so a head mounted camera would probably be sufficient for almost all practical purposes.