TNG was and is by any estimation a family show. Outside of Conspiracy only mild violence (and most episodes have none) and any sexual content was very tame even by 80's standards. TOS had considerably more sensuality on it (Orion strip show, Kirk blatantly having sex in several episodes) and aside from Conspiracy more intense violence (agony booth, Kirk and Spock getting whipped in Patterns of Force, exc).
Okay, first off, "Kirk blatantly having sex in several episodes?" No way. Not in the 1960s -- the censors would never have allowed it. It could only be implied, and the most blatant implication they ever had was Kirk putting his boots on after being alone in his quarters with Deela in between scenes. Generally, love scenes had to be presented in such a way that you could assume the couple never went beyond first base, and any implication to the contrary had to be extremely subtle. You couldn't even
talk about people having sex except in the most indirect terms. Heck, "The Mark of Gideon" acknowledging that contraception existed was startlingly bold for its day.
Second, you're forgetting the season 1 episodes like "The Naked Now," "Justice," and "Angel One" where Roddenberry took advantage of the freedom to include more skin and sexuality than he could've gotten away with in the '60s. As I've been saying all along, Roddenberry always intended Trek to be adult, and he was very much a fan of sexually themed material, but his successors on TNG dialed down the sexuality somewhat and made it more staid. It's an oversimplification to generalize about the whole seven seasons, because there was a lot of change and transition over the first two years.
And the phrase "tame by '80s standards" is poorly formulated, because there wasn't a single set of standards. By the standards of a 10 PM nighttime soap like
Dynasty, TNG was tame, but not by the standards of
actual family shows of the era. I just finished rewatching
The Greatest American Hero for my Patreon reviews, and it was definitely a family show, so much so that the main character and his girlfriend/almost-fiancee hardly ever touched each other on camera or showed any sexual friskiness, until season 3 when the show was briefly moved from 8 PM to a 10 PM slot. It also had little onscreen violence, with the bad guys usually being arrested rather than killed and murders usually taking place off-camera.
It's harder to push the envelope if you don't have a network behind you. Plato's Stepchildren and a lot of other things on TOS probably never get on the air if the show was syndicated vs being on NBC.
Oh, just the opposite is true. Syndicated shows could push the envelope more than network shows, because they only had the studio overseeing them instead of both the studio and the network; fewer bosses = fewer restrictions. I think I mentioned earlier that there was a 1990 episode of
War of the Worlds: The Series that had a startlingly racy nude bedroom scene, on a par with the kind of nudity you didn't get on network TV until
NYPD Blue came along 3 years later. And certainly
Deep Space Nine was more daring than
Voyager, because DS9 didn't have nervous network bosses pushing it to stay basic and avoid taking risks.