Assignment: Earth has about as much of a connection with Trek as Mork did with Happy Days, which is very little. However, Mork & Mindy was a popular spinoff, and A:E probably would have worked, because it was a Cold War type of story about preventing WWIII that was more accessible and identifiable to people in many ways than the more abstract concepts in Star Trek. Not only that, Robert Lansing and Teri Garr were well cast and memorable in those roles, that here we are today still thinking about it. I think in retrospect the show dates because the cold war is long over and a typewriter that types by itself is highly anachronistic, not futuristic, but within the context of its time, and in reruns in the 70s when it popped up again, it was pretty hip. I always enjoyed it as a kid and I didn't mind that the main cast were "wasted" within that one episode, since it was always going to be an unusual one.
I also think that by canonizing G7 as a time-traveler, it opens doors to have him show up elsewhere in Trek, which I think Trek fans just want to see happen, regardless of Gene's original intention. Since the series didn't happen, he can (in theory) be an occasional guest star elsewhere, which is interesting to ponder.