It couldn't have worked from a timing point of view without moving a good portion of the beginning of RotK back to TTT.
As Frodo, Sam and Gollum are climbing the hidden staircase, the armies of Mordor are marching on Osgiliath, en route to Minas Tirith. So, Orthanc, Pippin and the Palantir and Gandalf and Pippin riding to Minas Tirith and meeting Denethor would all have needed to be added in to TTT.
It only works in the books because the two storylines are presented sequentially rather than concurrently. But to do that on screen would have been incredibly confusing for audiences and would not have worked at all.
And I might as well tack on my usual refrain on such questions: What's done is done. We have what I consider to be three amazing films. Either watch 'em and enjoy 'em or don't watch 'em at all.
