I think you need to go back at least 10 years before Friends, possibly 20 or 30, maybe a lot more...100% noticed this phenomenon since the late 90's I call it Chandlerisation as Chandler from Friends seems to be the big influence for sassy, smart talking action heroes and other characters.
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Chandler might have influenced the look, but the base character is old.
The likes of Die hard* were doing the quips in "more serious" action films long before Friends, the likes of Batman were doing them in the 60's, and likes of the original Flash Gorden and other "serials" were doing them back in the 30's when you might have watched it before a film at the cinema.
It's been a character type practically since the birth of cinema, about all that has changed is you're probably more aware of them since Friends because that may have been when you were growing up/started paying attention, about all that changes is the language used and look gets updated to stay current.
Although a funny thing if you ever pay attention to a lot of film/TV set around certain times is that they'll often use modern hair styles especially for women (or ones that haven't ever really gone out of fashion), as they don't want someone to come of "frumpy" or "like your dad" because they've got a hairstyle you associate with your parents/grandparents/School teacher when the character is meant to be young, despite the fact that at that time it might have been a young persons/new/rebellious style.
I've watched quite a few films/tv series where I've thought "that character is based on X" only to fined that X might have been made 5+ years earlier.
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*Thinking about it, I'd possibly say that Chandler was based more on Bruce Willis in Hudson Hawk (4 years before Friends) in terms of the quips etc, but it's been probably 25 years since I last watched that in full.
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