The big reveal in Episode III is that the Big Bad, Wilhelm, is planning to reset time in order to stave off the end of the world. It is heavily implied (and supported by Word of God) that this isn't the first time this has happened- it's happened before, many, many times. Taking this into account, it would be easy to say that every work ever created is, in fact, canon with each other, with Xenosaga taking place at the end of the timeline. (Well, my headcanon is that Xenogears takes place after Saga, and 'Blade is set before both of them, but let's set that aside for the moment.) As Super Mario Galaxy has shown us, every time a Universe is reset, when it recurs, it is slightly different from the one that preceded it. Thus, every book, movie, tv show, video game, ballad, legend, myth, what-have-you is true, and actually happened on a previous loop. This naturally includes Xenosaga, the Animation- that's how events played out on a previous loop. Heck, this may even extend to fanfictions (though the idea that My Immortal is actually how the Harry Potter series played out in a different loop might make one shudder.) Naturally, this makes the canon Xenosaga games the very end of the timeline (excluding my headcanon that 'Gears comes afterwards,) because that's where the loop is broken, and the universe finally proceeds past those events. For real fun, you could even say that we're on an earlier loop as well- have fun thinking about that one when you're trying to sleep at night.
That's why Abel and Nephilim look like Abel and Elly, Xenogears Abel looks like his father as a kid. Abel and Nephilim found Lost Jerusalem, did whatever they were supposed to do there, then Abel decided to become a spaceship captain, because you can't be the Messiah all the time. They got married, had two kids, then the Xenogears prologue happened.
...was Allen. As one of the only main characters to not have any direct involvement with the trilogy's many conspiracies, along with having none of the main party's fighting ability, he serves as a representative of the every-man in the Xenosaga universe. In other words, not somebody likely to strike Wilhelm as "significant" enough to keep a close eye on. Despite this, he somehow finds himself dragged into most of the major events that occur throughout the series. There were plenty of opportunities for him to die, whether as far back as the Woglinde incident or any of the attacks by Ormus/U-TIC. In fact, he almost certainly did in all the previous cycles. Or perhaps instead of dying, he chose to duck out at some point. Either way, in previous cycles, he wasn't around for the third game's finale.
What changes with Allen out of the picture? There's nobody to convince Shion to turn away from Kevin. The two either take down or heavily weaken the rest of the party when they battle outside Zarathustra's chamber. With the party out of the way, nobody is left to stop KOS-MOS from delivering the last piece required for Eternal Recurrence to commence. Time is reset, and the cycle begins again.
Allen's continued existence in the face of all the life-threatening shit he deals with represents the evolution of the collective unconscious. It's possible that, with each cycle, Allen stuck with the party further and further throughout the trilogy's storyline. His surviving all the way to Michtam represents the evolution of the collective unconscious to the point where it is ready to reject Wilhelm and continue existing without him.