As an Australian citizen, whilst the police here aren't perfect, I also believe they aren't as trigger happy because, quite frankly, we don't carry guns on our person in Australia. This means that when police make a routine stop because of a broken tail-light they aren't as likely to feel like their life is in danger, and this almost certainly means they hesitate to fire their weapon unless they are really in danger. They are also aware that if they do discharge their weapon then there is a full investigation done. The investigations are quite thorough and actually normally very fair, but no police officer wants to be investigated really and all police officers know what a serious thing it is to fire their sidearm.
I don't expect any citizens of the U.S. to agree with me. But it occurs to me that as more people carry increasingly powerful weapons, the police have had to upgrade their own weaponry, body armour and tactics in response. From my vantage point here in Australia, it puzzles me why this isn't obvious: the more people who carry guns, the less likely law enforcement will try to negotiate and use minimal force.
From my perspective, America's gun culture is bizarre.