> A situation that could be minimal risk to everyone (because let's not pretend that people shooting at cops entering a home is a usual thing), is now high risk (and traumatic in all cases) for the citizen.

Well, if you are arresting a person, perhaps there's things that can be done, like waiting outside. How is it supposed to be handled when you have to get evidence?

> I would sure be less freaked out in Europe

I'm sure this is an oversimplification but AFAIK states in Europe either have more restrictions on gun ownership or a culture/mediascape/welfare-state that doesn't encourage the desperation/antagonism you see in the US.