I'm just gonna throw out some possibilities to jumpstart discussion:

(1) Tesla's machine is merely a transporter (not a replicator), therefore Angier has to use Root as a double for the trick.

(2) Tesla's machine is a sham that doesn't work at all (other than as a light-show prop), so Angier has to use Root for a double.

(3) Tesla's machine works as a replicator, but the clones created are inanimate (like in the book). Furthermore, Angier loses his identity/soul over repeated replications over time and becomes a more of a ghost of his former self each time he uses it.

(4) Merge the Borden twins into a single person and never reveal how he pulls off the trick. [While this would alter a major plot point of the movie for the final reveal, I think it could be viewed like an actual magic act, where you're not supposed to find out how it's accomplished. Therefore, Angier's obsession to figure out the trick is never realized).