Getting the air out of the MC bore is necessary, no matter how it gets done. Since there's no mechanical connection between the pistons in a double reservoir master cylinder unless one end fails, bench bleeding can be a challenge. Usually one chamber will purge itself of trapped air before the other. Then there's a hydraulic connection instead of a mechanical one to make the second piston move. When one piston or the other loses its ability to push fluid, or there's a leak downstream that empties one reservoir, then the pedal drops by about 2/3 of its travel, the pistons in the MC touch each other, and the intact fluid circuit does all the braking. If a constant gentle pressure on the brake pedal causes it to fall away slowly, that's an impending master cylinder failure warning you to do something about it.
Jerry