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Conversely, I wince everytime I'm called 'sir' in an American restaurant or shop.

Oh, I never thought about that. In the UK, is it improper to call someone Sir who isn't a Knight?

Pretty much.

Used outside that frame it’s an insult as in:

You, sir, are a cad and a bounder.

Uh, no it isn't.

Not at all, for example at secondary/high school you would address male teachers interchangeable as ‘sir’ and ‘mr. Last name’.