I seem to recall several highly professional conversations occurring in runabouts and shuttlecraft during TNG and DS9...
I can't tell if you're being serious or sarcastic. I will remind you that I was comparing TOS and nuTrek. But if you insist on bringing TNG into it, even Wesley usually displayed more maturity on duty than the characters did in the Abrams movies.
And DS9 whether one liked it or not was a successful show, closely comparable in its pop culture profile to the X-Files. About as many people know who Sisko was as know who Scully and Mulder were.
Way back when NonCon was still going strong, there was a year when it was held in Banff. Somebody had added a nice amount of filk-related programming to the schedule, and since I enjoy that, I jumped right in. I found myself with a group of people who wanted to write a filk on the spot - all of us contributing - and chose to do it using a Beatles melody and an X-Files theme.
So here's me, who has written many Star Trek filks, and a respectable number of filks based on other fandoms - including based on non-televised/movie SF novels - and I'm not very familiar with most Beatles songs and had never seen even a single episode of X-Files. I was lost and confused for most of that session and had to get everyone to explain the concept of the series, who Scully and Mulder were, what their relationship was to each other, and so on. Anyway, I was finally able to contribute a grand total of ONE line to the song, which was based on the Beatles' song "Help!".
Point of the above anecdote: Never assume that a genre program that makes it into popular culture is familiar to everyone, even SF fans.
During the run of ENT, I remember watching Jeopardy!, and this question popped up: "This series features characters like Archer, T'Pol, and Dr. Phlox." Long pause, blank looks. Then a woman buzzed in, big smile beaming, and called out with perfect confidence... "What is Spongebob Squarepants!" That's how popular the non-TNG Trek spinoffs are.
Again, that's not to say anything at all about quality. Let's just be realistic about the minimal impact DS9 has made.
Then again, the vast majority of people who make it on to shows like Jeopardy! are really not that knowledgeable. I recall one time when the right question was "What is the Sun?" (the answer was "The nearest star to Earth") and the woman who buzzed in looked vacantly into the air and mumbled something about "Omega?"
Alex Trebek was noticeably startled at how somebody could be so ignorant.