Yep, I remember that Love American Style segment: "Love and the Happy Days"--which I suspect may have been a backdoor pilot for the later TV series.
My impression is that a ton of L,AS segments were either backdoor pilots or failed pilot films that the show was used to burn off. Wikipedia says it also spun off a sitcom called Barefoot in the Park (though that's based on the Neil Simon play, so it's questionable) and an animated Hanna-Barbera sitcom called Wait Till Your Father Gets Home.
I think a number of TV anthologies have included the occasional backdoor pilot; I know a couple of The Twilight Zone's really inept comedies, like "Cavender is Coming," were intended by Serling as backdoor pilots for fantasy sitcoms (one of them even had a laugh track).
Spinoffs have always been a huge part of TV cross-promotion strategy but they didn't give two shows the exact same name with different things after the colon. That's a precedent that has taken the burden of at least having to give shows their own identity off of the networks.
Granted, the Trek shows did begin the modern trend of using a Franchise Title: Series Subtitle format for the various shows, but that's really a minor stylistic innovation on a longstanding practice. And it wasn't completely without precedent: see The Man from U.N.C.L.E. and The Girl from U.N.C.L.E. There was also a 1956 British anthology show called Armchair Theatre which spun off an Armchair Mystery Theatre in 1960. In both cases, the spinoff ran simultaneously with the original (and was outlived by the original).
And there are examples of sequel/retooled series that reused part of their originals' names, like M*A*S*H and AfterMASH or Three's Company becoming Three's a Crowd. Or The Brady Bunch spinning off the animated The Brady Kids and having sequels called The Brady Bunch Hour and The Brady Brides, all predating TNG. Not to mention all the annually retooled Saturday morning cartoon franchises like The Archies, Super Friends, and Scooby-Doo, with each new incarnation of the show using a variation of the title. Sure, that's not quite the same as having multiple simultaneous series with a blanket franchise title, but it's a precedent that had to evolve only slightly. Nothing "new" comes out of nowhere.