This is a whole tangential subject but at least in UK TV terms that would not have been the case for Columbo, as it seemed in perpetual rotation with Kojak, Murder She Wrote and 80s and 90s Perry Mason throughout the 1990s. The last really big US series that I remember getting a huge push from start to its very finish was Buffy The Vampire Slayer (with even its Angel spin off getting shown on another channel).
But yes, I only really know the Saturday Night Live stuff from the films various cast members made afterwards. Which made things like Coneheads seem rather inexplicable at the time! (I remember for a while thinking it was ripping off of the premise of the, actually far better,
Meet The Applegates, when it probably was the other way around!). Yet it very much depends on the whims of the people buying stuff for television as I certainly remember in the 1980s staying the night and watching The Equalizer, Midnight Caller and L.A. Law with my neighbour when my parents were working night shifts! And Married With Children got a lot of airplay as did, um, The Cosby Show (I was more of a fan of Hangin' With Mr Cooper myself).
I wonder if that UK/US gap has widened a little bit in recent decades with the rise of Sky pilfering all the 'big shows' that at least for me made a mockery of following both Lost and The Sopranos, as they both left free to air, never to return. Mad Men suffered the same fate too when Sky did that contract to pick up all HBO content (which of course meant Game of Thrones has never touched free to air). The Wire was probably the one exception in the last decade and even that came to the BBC a decade late and tossed away in daily late night double bills in that same 11.30 p.m. post-Newsnight slot that Seinfeld (and The Larry David Show!) got thrown into.
I think in the wake of tabloid complaints of lots of material being bought in that the BBC in particular has made it a policy not to fill up schedules with American imported shows in order to create 'homegrown' content that justifies the licence fee more. Similar to the policy of seemingly dropping anything in black and white from being broadcast except on the rarest of occasions. So we're never going to see things go back to the way they were in the 90s with Buffy, The X-Files, Star Trek: TNG and DS9 (even Voyager, which got a whole Star Trek night devoted to the screening of its pilot episode!) and Murder One being actively promoted in primetime slots the way that they were, and definitely not on BBC1 at all (BBC2 still does a few things with Pose and those American Crime Story series on occasion. And BBC4 does the whole Ken Burns thing for the new series, but often edited down)
Channel 4 mostly has moved away from that too, probably having learnt its lesson after the previously mentioned Sopranos and Lost plunderings from Sky. Though it did itself pilfer The Simpsons from the BBC in the early 2000s and keeps that in really heavy rotation in primetime still (though still about five to six seasons behind the US), and it does also have that E4 channel to mostly ghettoise American import shows into instead (The Goldbergs and its spin off Schooled, Brooklyn Nine Nine, The Big Bang Theory, How I Met Your Mother, Gotham and recently all the Adult Swim shows and Star Trek: Discovery too), though even there it hides stuff away such as for instance the whole of the most recent series of Fear The Walking Dead being blown through with no promotion at all at 2 to 3 a.m. slots (!) on week days (!!) in the last fortnight.
That actually makes me think that The Simpsons is probably the best test for international ubiquity! I guess that exports everywhere still?