BASED ON MY OBSERVATIONS IN PRACTICAL SHOOTING GAMES WHERE COPS PARTICIPATE:
I actually think better firearm training would reduce the number of incidents in which well-intentioned-but-mistaken cops shoot various people who are not actually a threat. Most cops have a painfully slow draw and very poor indexing. They usually can hit things when they shoot slowly (reflective of what most of their quals require), but they cannot do it very fast. Those who hang around the gun games usually get fast, just like anyone else, but the average cop is painfully slow on the draw, transition, etc.
Now, consider a situation in which a cop is trying to decide whether a suspect in a poorly-lit environment has a gun in waistband or just a folded up baseball cap. The shorter the time between the cop deciding to fire and landing hits, the longer the cop can afford to wait. That extra tenth of a second may provide the additional information needed to decide not to shoot at all.
I think police agencies ought to require cops to at least show up and watch a few USPSA or 3gun matches so they can get a sense of how fast ordinary, non-pro shooters can learn to go. Many of them simply have no idea.