One of the features of modern life (well, my modern life) is the ubiquity of the American sitcom. We now have whole channels whose main selling point appears to be re-running the likes of Friends, How I Met Your Mother and The Big Bang Theory, but not necessarily in the right order. Of course, plot sequence isn't that big a deal in a sitcom. Indeed, to judge from the ridiculous denouements of most US drama series, narrative coherence isn't any sort of priority, and hasn't been since Bobby Ewing's "dream year" in Dallas.
In the late 70s and early 80s US sitcoms were a rarefied taste, with gems such as Taxi or Barney Miller often buried late night on BBC2 or Channel 4. Before multi-channel TV got to double digits, we even had the pleasure of re-runs of The Phil Silvers Show, which made a change from Terry and June. The mid-80s saw the start of the decade-long hegemony of Cheers, superseded in the 90s by Frasier and Friends. These behemoths exhibited what became a recurrent structural problem for sitcoms, namely the need to suck dry every smidgen of possible backstory in the search for new plots. Family members would suddenly appear out of nowhere, as if they'd been in a witness protection programme for years; old lovers would resurface, provoking much angst (in real-life, this would just provoke a fight); old schoolfriends would materialise, wanting to right old wrongs or pick old scabs. Yadda, yadda.
In contrast, British sitcoms of the 70s and 80s seemed to make a point of keeping the back story off-stage. The simple explanation is that they tended to have many fewer episodes, and were thus less ravenous for plot devices. Steptoe and Son and Till Death Us Do Part both had fewer than 60 episodes, while Whatever Happened to the Likely Lads ran for only 27, and Fawlty Towers for only 12. In contrast, Cheers, Frasier and Friends all had over 250 episodes. Even those British shows that ran for the best part of a decade, Dad's Army and Only Fools and Horses, only notched up 83 and 71 episodes respectively.
I think there is more to this than the need for the regular injection of plot stimulant. What is notable is the way that the British shows made use of off-screen elements to provide context and depth, rather than just an excuse for a guest appearance by Elliot Gould or Brad Pitt. It probably sounds pretentious to cite Beckett's Godot in this regard, but the off-stage presence exerts a powerful influence, but only while it remains off-stage and therefore uncertain and unresolved.
In many cases this background revolves around women, which probably reflects the fact that the protagonists (and writers) were invariably men. In Steptoe & Son, the wife/mother is the key absence. In The Likely Lads, the entire series was built up from the back story of Terry's army tour in Germany where he has left a wife who is never seen. In Minder, "er indoors" is frequently invoked as an invisible power.
Probably the most interesting (because uncertain) example is in Dad's Army. Why doesn't Sgt Wilson marry Mrs Pike? The matter is never directly discussed, though everyone accepts that he is her common-law husband and the father of young Frank. Eventually, in the 5th of the nine series, Wilson reveals to Fraser that he has a daughter from a failed marriage. We are left to assume his wife would not grant a divorce. Nothing more is said but you get the sense of an entire life beyond the painted backdrop.
What I think this shows is that British comedy can accommodate pathos, being often a study in failure and the consoling power of delusion. Many idiot Brits claim that Americans don't understand irony, which is not merely absurd (like claiming they breathe funny) but ignores the fact that almost all of US comedy is actually over-reliant on irony, and not just the verbal, wisecracking sort. What US sitcoms struggle with is pathos. Any attempt almost immediately collapses into maudlin sentimentality, which is why Last of the Summer Wine is the British sitcom that, despite its Yorkshire parochialism, is at heart the most American - all 295 episodes of it.