Many shows have eliminated characters without explanation. Friday Night Lights wasn't the first nor was it the last. Out of all the shows that have written out characters without so much as a passing reference, Saved By the Bell takes the cake for sheer lack of concern for continuity.
In its earliest incarnation, Saved by the Bell was called Good Morning Miss Bliss. This show featured Zack, Screech, and Lisa, but they were secondary character to a hot teacher, the titular Ms. Bliss (Hayley Mills). Season two saw the departure of Mills and two other teacher characters. Three student characters were swapped out with Slater and Jessie.
Later in the series, a character named Tori, complete with a cool black leather jacket and 'tude, was added to replace Elizabeth Berkley and Tiffany Amber-Thiessen when their stars grew too bright for Saved By The Bell. Tori lasted half a season, until she was booted for the final graduation episode, for which Thiessen and Berkley returned. None of this was explained anywhere in the scripts for the series.