I liken TAS is be inspired by or loosely based on real TOS canon with the disclaimer, "Stardates, conversations, and technical details may be simplified or fictional but the mission events occurred."
That's basically what I think about
Lower Decks, and about seasons 3 & 4 of
Strange New Worlds.
Although really, apparently Roddenberry himself considered TOS to be a fictionalized, occasionally inaccurate dramatization of the
Enterprise's "real" missions, judging from his introduction to the TMP novelization and his advice to TMP viewers to accept that Klingons had always had ridges and TOS had just depicted them inaccurately. After all, Roddenberry got his start in TV adapting real police cases to be dramatized by
Dragnet. And once I realized that, it occurred to me that TOS was a lot like
Dragnet, in that both shows were framed by narration representing their main characters' official reports of the depicted events.
Not as much as you might think. In the first place, "family-friendly" is not the same as "specifically made for children" or "of no interest to adults"
I don't accept that distinction. After all, ideally, parents would watch along with their children. I mean, parents would generally need to take their kids to a movie theater (unless it was a neighborhood theater within walking distance, like the one near my childhood home before multiplexes crowded out the local theaters), and it used to be that there was generally only one TV per household so the family would watch together. So I don't accept that there's a wall between "for children" and "for adults." Children's stories have always been told with the expectation that parents would experience them too.
Also, the people
telling the stories are adults, and consumers of fiction often fail to consider that the creators of fiction are people who want to enjoy their jobs. So
of course the adults who tell children's stories want to tell them in a way that they themselves would enjoy. That's why so many children's stories have always been full of adult humor that goes over kids' heads, whether political humor or sexual innuendo or allusions to past pop culture from the adults' generation, or simply have intelligent writing and characterization that adults can enjoy too. (Heck, I kept watching
Sesame Street well into my '30s because I enjoyed the humor that tiny tots wouldn't have gotten, and I'm currently a big fan of the Japanese
Precure anime franchise aimed at young girls because the stories are just so well-written and well-made.)
(and remember, the original Airport was released with a G rating, as was 2001 and ST:TMP).
Because at the time (at least for the former two films you mention), "G" meant "General," intended for audiences of
all ages. Anything that wasn't too violent or sexy or profanity-laden for general audiences -- basically anything that would've been approved for release during the Hays Code era -- was given a G rating even if it was aimed at adults. (After all, a lot of adults might not have wanted to see overt depictions of violence, sex, or profanity, so the ratings were meant to tip them off as well.) The idea that the G rating was
exclusively for children's films developed later, because PG films (and later PG-13 films) were perceived as more profitable and desirable, so filmmakers started slipping in gratuitous cuss words and such to get a higher rating for films that otherwise would've been rated G, and so eventually the only G films left were the children's films.
The problem with any argument based on letter ratings is that their meanings have shifted so far over the decades that they're essentially useless for comparison purposes. What we think of as PG now would've been G in the '70s or '80s.
And indeed, while every live-action broadcast television iteration of ST (and arguably, TAS as well) was intended for adult audiences, they were all (at least in my extended family) always considered family-friendly, and more family-friendly than a lot of other broadcast television.
Well, of course, because all free, over-the-air commercial television could be watched at any time by any member of a family, so it all had to be suitable for all ages, with even the most adult-oriented content being no more than the equivalent of a PG movie. The thing is, in modern times we've gotten so used to "adult" TV being the stuff on pay cable and streaming with explicit violence, language, and sex that all commercial TV seems tame and family-friendly to us by comparison, in the same way that all Hays Code-era films seem tame in comparison to the MPAA era when more explicit content became allowed with the PG and R ratings.
And TOS was not "more family-friendly than a lot of other broadcast television." On the contrary, it pushed the envelope for skin and sexual content by the standards of its day. But the Sexual Revolution was happening around then, and the R rating was introduced around then, so what was seen as racy by 1966-9 standards had come to be seen as relatively tame by the time TOS became big in reruns in the '70s.