Except the film already has multiple climaxes and denouements to rapidly diminishing returns.
I agree with this complaint. Where I disagree is the implication that adding the Scouring of the Shire would have come across as anything other than just one more denouement.
The problem is that a movie is consumed all at once, which means that you have to keep the audience engaged throughout. There is no chance for the audience to come down off a climax, process it, get some distance, and return ready to engage a new arc*. And that means, once you have the grand climax of Sauron's defeat,
anything that comes after it is going to feel inconsequential. The end of the movie drags on as it is, despite Jackson doing everything in his power to compress it--if you tried to work in the Scouring of the Shire as well, the audience would either fall asleep or leave.
A book, by contrast, is usually consumed in pieces over a span of days or weeks. Those who can plow through a whole book in one epic sitting are a distinct minority. Given that "Return of the King" goes on for six full chapters after Mount Doom, it's likely that the reader will get at least one break in between Sauron's fall and the discovery that Saruman has trashed the Shire. This allows the sense of scale to reset, so that the Scouring seems meaningful.
A TV show is like a book in this regard, and could pull off the Scouring in a way that no movie ever could. It could also include more of the foreshadowing that Tolkien uses to lay the groundwork. The movie version of "The Two Towers" couldn't really justify giving space to the discovery of Eastfarthing pipe-weed in Isengard, but in a TV show, it would be fine.
*Okay, yes, it's a trilogy of movies, so the audience does get two chances to do this. But that's no help in this case.