Some of the finest comedies on British television were very stagey - Dad's Army, Fawlty Towers, Porridge, early Red Dwarf, Father Ted, Blackadder. I think it's still a functioning model. There are other comedy models of course - pseudo-realist (like The Office) and horror-drama (like Psychoville or Misfits).
Successful comic film works very differently from successful TV sitcom: in the funniest films (of the TV era) everything falls completely apart, and the world of the film is exploded. I'm thinking Blazing Saddles, The Holy Grail, Airplane, Galaxy Quest, even (more gently) Spinal Tap. Perhaps TV sitcoms don't transfer well to film, and on telly have not become film-like, because the film model is about destruction, while the sitcom is about continuation. It's interesting that only Monty Python has transferred successfully from BBC to film, because it was one of the few TV shows that destroyed itself every week, usually several times in each episode.