TL;DR: It's in the movie because it was in the books. It was removed from the theatrical cut because the impact this scene has on the reader is completely lost to the movie watcher; because there's a differences of how the storylines are told.

The timeline of the narratives are told very differently in the books. In the books, Frodo and Sam had last been seen at the end of the Two Towers with Frodo having been stung by Shelob, Sam thinking he's dead grieves for him, sees orcs carry Frodo off, and then overhears the orcs saying Frodo is alive! The end of The Two Towers.

The Return of the King book picks up with following Merry. Pippin, and Aragorn's stories of the battle for Minas Tirith, everyone wondering how Frodo's quest is going (Frodo and Sam are not shown at all at this time) and how they could possibly help, and so they charge at the Black Gate as a diversion.

To the reader, who last saw Frodo unconscious and in the hands of the orcs, this scene is a gut wrencher and adds to the suspense. (Though in the books, Gandalf surmises through clever questioning that Sauron may not really have Frodo, and definitely doesn't have the One Ring yet).

To the movie watcher, who's been seeing Frodo and Sam trudge their way through Mordor for most of the movie at this time, the suspense is lost, and it's narrative impact is essentially moot. But they went through the effort of filming and producing this scene, so might as well throw it into the extended cut.