I just find sharing one life is more difficult and mentally draining compared to creating two new identities: one of the twins will be Fallon and the other will be Alfred the whole time.
When they are on the street, they could live their new lives, but when on stage, they could switch with one another so both can get the spotlight. Their plan just doesn't make sense to me.
Being the one twin who has to disguise himself constantly and therefore not really have anyone close to them who can tell that they are really a twin of Borden seems unfair to them. They cannot disguise themselves in any permanent way (such as by growing a beard or changing hair style or anything like that) because of having to be on stage as Borden. So it all has to be wigs, makeup and costumes.
I imagine that (except when getting into/out of disguise) at any moment Fallon does everything as Fallon, including sleep, in case they are accidentally discovered, forced to leave the house because of a fire etc. For Fallon to have a relationship would require his partner to be in on the secret which I imagine would not be acceptable to Borden/Fallon.
To share the responsibility for being Borden and Fallon seems more fair on them.
If they allowed themselves to live as one or the other it becomes harder to ensure that they look and act exactly the same at all times, especially when on stage. If they can live some of their life as Borden when not on the stage, the stage show itself almost becomes trivial.
Even swapping every day(?) they sometimes slip a little, and Sarah (Rebecca Hall) unconsciously notices when its not her Borden. Imagine what might happen if she encounters the one who is usually Fallon backstage. What more opportunities there may be to slip up and reveal it is not her husband if he spends little time with her and their child.
The story shows us continually that there are two people playing Borden, with clues like the hand injury getting worse again, or which one loves Sarah (Rebecca Hall). We see him devoted to his wife one moment and having an affair with Olivia (Scarlette Johansson) the next.
To have one as Borden and one as Fallon would not give us those clues. There would be no affair with Olivia, no suicide of Sarah. This massively diminishes the shock of the reveal, the magic trick they have performed on the audience, when we see the depth and dedication in what they did.
The whole point is to stay in character to facilitate the illusion of magic
Yes, pretending to be a single character is very difficult and mentally draining. But they don't do this just for fun but to enable a major magical illusion. They are motivated by the art of magic.
The clear hint that this is the purpose is hinted at in the early discussion between Borden and Angier where they try to analyse how the "Chinese" magician whose show they view is able to perform the fish tank trick. They observe him during and after his show. They try to reproduce the trick. And, once they get some understanding of how he achieves the trick (which involves–if I remember correctly–somehow supporting the large fishbowl between his bowed legs) Borden observes that the big secret to the trick is that he stays in character even when not performing. The chinaman walks awkwardly with bowed legs even when not performing the trick masking the feature that is necessary for the trick to work by making it look like a normal feature of his body.
The commitment to staying in character is an essential part of the distraction involved in the trick.
Later in the movie as Borden's trick with the transported man is revealed, we realise that twins living the illusion that they were just one person was the essential commitment to hiding the secret behind the trick. Borden has trumped the Chinaman in his commitment to the illusion. The cost of living in character is huge. Bodily mutilation has to be shared. Their love life is a mess. One twin eventually dies. But their joint commitment to the illusion is what enables the greatest magical trick of their era.
Yes, pretending to be one person is a huge painful commitment. But their goal is the greatness of the magic trick this enables. Their obsessive commitment to the art is motivation enough.
