In the book, while Frodo and the Fellowship were on their quest, the Shire was exploited and almost ruined by Suraman and his cronies. Jackson left this and the triumphant return of Frodo, Sam, and the now burly Merry and Pippin and their battle to reclaim the Shire out of the film. I was hoping to see it added to the extended version of the DVD, but it was not. Did Peter Jackson explain why he omitted this portion of the book from the movie? If so, what was the reason?
Generally speaking, it seems that Peter Jackson doesn't really like that part of the book, and it also seems that Tolkien himself intended the chapter to represent a local situation in England, which contrasts heavily with the universal symbolism of the Eye, the Great Enemy, the everlasting confrontation of good and evil, etc.
The big argument to justify the omission can be summarized as
Nevertheless, it also seems that there is no official explanation from Peter Jackson on this subject, so this is just speculation from fans.
As for this part of the story being included in the extended version, consider that even the non-extended version of the movie has a very long ending, and that the extended edition is 20~30 minutes longer even without major additions. A whole new subplot and a battle would be too much.
In my opinion, The Scouring of the Shire would be a lovely short film to watch, especially if directed by Peter Jackson in the same spirit as the other movies, and even more so if the same actors were used. We could see the four hobbits being the leaders on the battlefield, Frodo reluctant to the idea of violence, the chief, an ugly Shire (e.g. fewer trees, no inns), etc. A longer film could probably involve later events, like Sam's "garden" (with Galadriel's seeds), Sam as the Mayor, Merry as a writer, Pippin being called to Gondor by the King, etc.
As it is, Return of the King has two major climaxes: the battle at Minas Tirith, and the destruction of the ring in Mount Doom. Aside from the extra time involved, a third climax would likely be overwhelming for the viewer; besides, it wasn't essential to the main storyline.
Something I recall, from the bonus DVD included with RoTK: Extended Edition, is Viggo Mortenson recalling a conversation with Jack Nicholson. It was to the effect that Jack hadn't seen the actual end of the movie, he left before that to warm up the car for his family. Jack commented that the movie had 'too many endings.'