I'm not sure that would have worked. If you take Sauron out of Mordor, then he probably takes all of his army with him. Meaning that the ending would be Frodo and Sam strolling across an empty plain towards Mt. Doom while Sauron's entire force crushes everyone else at Minas Tirith. Frodo and Sam destroy the Ring, defeating Sauron, but die in Mt. Doom, which doesn't matter because everyone else has died already anyway. Kind of a
killer ending.
