How is the camera going to record what prompted the officer to pull his gun in the first place?
Excellent point!
What you see is a man with a knife....What you don't see is that he's standing at a butcher block in a butcher shop.
Since its split seconds, whatever prompted the cop to pull his gun, will still be in view when his gun is pulled, i.e. the situation isn't going to change in 1/10th of a second.
That said, I talked to one of my friends who is a cop, he kind of likes the idea, but his only concern is that other cops may now pull their guns faster or be quicker to draw, just to get the recording started.