Sure, I'd agree that US police are probably recklessly trigger happy. But when it comes to warning shots their policy is correct.

I think the core of the issue here is a societal difference towards firearms, and how that results in the training and education of people. Gun ownership is fairly high in the US, relative to Europe and seen as a right having requisite responsibilities within some circles. One of these responsibilities is training in the use and handling of firearms. From childhood on, I was always taught to "never point, and most definitely never discharge a firearm at anything you do not specifically intend to kill." Most of the ranges I practice at have the same sort of messaging ubiquitously placed on the site.

While I can't speak to the experiences in Germany, I would presume that a society that largely eschews the personal possession of firearms would have a built-in perception that anything is better than pointing one at a person. Whereas, in the US we might argue that the weapon should not be drawn unless you have every intent to take a life. (Outside of practice towards targets.)

I also think that criminals have a different attitude towards warning shots knowing that the police (almost) never fire shots.