BTW how would you talk to the said cop? Officer?
I'm from Southern Europe and I'd say it's quite normal for waiters to greet customers like that (except on fancy, expensive places of course). You don't have to "create bonds" with them, it's just a matter of being friendly.
Also, don't forget that waiters in the U.S. live off their tips, so I guess that can be a reason as to why they try to be as friendly as possible.
When interacting with authority figures I am generally polite without deference.
I find that people generally use honorifics when they're being quite rude and would like to soften the impact (e.g. the perennial "Good day, sir"), or while insipidly attempting to endear oneself to another (e.g. perceiving someone as wealthy or powerful). I don't know if it's my own egalitarian nature, or cultural, but I find both more rude than the omission of "sir" or "madam".