I get the scouring has some themes worth hitting, but lets be honest, the pacing of the book is all sorts of messed up. Even cutting the scouring there is a ‘too many endings’ thing going. Certainly the scouring was a chance to show the growth of Merry and Pippen, which is probably the biggest loss, but it would play poorly on film. Either you don’t do it justice, and do it in 5 minutes, or you tack half an hour into an already long film.
I just don’t think there is a way to do it without compromising the film or the story. We come off the grand global scale conflict that is resolved, and end with a small scale conflict that lacks the same tension and urgency, especially since the ones fighting it were critical pieces of said global conflict. The book just doesn’t really properly scale down the conflict, to show the more personal stakes. It is, I feel, one of the lower quality inclusions in the book.
As you note, Tolkien’s prose is of a different style, but often not up to that task. Honestly his style works better for the type of stories that the Silmarillion tells. Because his interest is not in the action, not in the intrapersonal, but rather on the world. How the sweep of history changes peoples, changes civilizations. How languages evolve, how history passes to legend, and how the stories change in the retelling. It is what he did best. LotR is at its best in scenes like the gates of Moria, it is a scene that Tolkien could do better than almost any before, or since. Because it is that history and legend driving the story in the now.
As for the core of the natural world, yeah some is lost. I personally would have loved more on Fangorn, the Entwives, and the destruction of Saruman. But the reality is I think that, from a movie perspective, the scouring of the Shire would feel a bit of a repeat of themes, one that adds another conflict in what is the dénouement.
Personally I would still rather argue the finer points of the LotR trilogy than The Hobbit because… I got bored with the first and never watched the other two.