"Do you really want every speeding pull-over to become a wild-west situation? Maybe your kids are in the car!"

That sort of thing depends on what is "normal". Many states in the US could have around 10% of the population carrying a firearm. Armed interactions with the police are common and the vast majority are a non-issue. The typical police response to "I have a license to carry and a firearm in the vechicle" is typically "Where is it? Just don't touch it". Happens all the time.

Now, is there a statistical difference? Maybe. It's hard to say because you would need to apply the same policing culture, legal system, and population dynamics to a lesser armed country. I don't know of any good choices for that combination.

More than half the country doesn't even require a license to carry anymore, and mentioning it in those states also doesn't typically warrant anything more than an "alright just don't touch it."