The dog thing is important.
Some people try to defend American police by saying that more people have guns in the US, so American police have more reason to fear that a suspect might be armed. But even in Texas, the dogs don’t tend to carry guns- American dogs are no more dangerous than those anywhere else. The difference is the culture within the police forces.
(I have heard that German police do shoot a reasonable number of animals- for instance, the widely-quoted statistic that German police only fired 85 shots at people in a year also says that in the same year they fired almost 9000 at animals. However, this seems to mostly be euthanising animals that were hit by cars.)