And there we have the crux of the matter. Should a writer ever have to do anything? No. Is there any style of writing that is objectively "wrong"? No. Are there certain things that make certain types of stories more enjoyable to certain audiences? Yeah.
Action/drama/adventure stories, for instance, tend to benefit from an aging cast. Not necessarily an extremely fast aging process, but a realistic portrayal of the passage of time. The in-story progression of time doesn't have to sync up with real world progression of time, it just has to sync up with the events that occur in the story. For instance, all three seasons of "Avatar: The Last Airbender" occur over the period of about a year. Aang, as a result, ages from 12 to 13 (and the other characters likewise). Aging benefits this kind of story, because it helps you take the fictional world more seriously.
On the other hand, comedy/satire isn't necessarily helped or hurt by aging. If the Simpsons writers wanted to, they could age the characters without hurting the show. They can also keep the characters the same without hurting the show, because it doesn't matter how time progresses in the Simpsons world. The Simpsons world isn't meant to be taken seriously, its there for laughs.
Do you want your fictional world to be taken seriously (at least to some degree)? Then your characters' aging process should sync up with the in-story progression of time. Do you want your fictional world to be purely for laughs? Then go ahead and have as many episodes and as many Christmas specials as you want while keeping your characters the same age.