The books of The Lord of the Rings have several side-adventures and subplots which greatly flesh out Middle Earth and the characters of the story, but would add quite a bit of time to an already epic-length movie trilogy (yes, Jackson added his own subplots to the movies which ate up more time, but my point still stands).
For example, Tom Bombadil added very little to the story as a whole, serving primarily (in the grand scheme of things) to provide the hobbits with their blades. Aragorn did the same thing in about five seconds on screen.
The Scouring of the Shire tied up some loose ends: where did Saruman go after he left Isengard? Gandalf mentioned that Sauron would eventually turn his attention to the Shire, if nothing else because while hobbits are of very little concern to him, he would take pleasure in their slavery and strife. Furthermore, Frodo saw death and destruction in Galadrial's Mirror. What happens to the Shire? After over a year of adventuring across lands the hobbits only heard of in stories, how have they matured and grown strong? This part of the story ties up all of these questions very decisively.
However, the story as told by the movie is focused on the destruction of the ring. The Scouring of the Shire could certainly have been included and would have been an interesting second climax: just when you thought the story was over and the heroes could go home, the heroes find their home under attack by villain #2. However, the movies were already very, very long, and several parts of the story had to be cut to make the movies a reasonable length to sit through in the theater
and to provide more screen time for Liv Tyler. By killing Saruman at Orthanc in the movie, his story arc in the Shire never transpired and that whole subplot could be cut.
TLDR: time. While the subplot did tie up loose ends and demonstrates how the hobbits grew from "little people" into brave warriors, it was not absolutely essential to the story of destroying the ring and its omission made it easier to sit through a movie that was already difficult enough to sit through without a bathroom break (in the theater).