I thought it was mentioned somewhere that dimensional splits were rather rare circumstances in the Chronoverse. If that's the case, I have a theory I find somewhat interesting.
If dimensional splits are rare, the best place to create one is where a piece of another dimension already exists. That is to say, Belthasar initiated the Time Crash having calculated that not only would Lavos pull Chronopolis back in time but that the planet would do the same with a piece of another dimension; Dinopolis. It was then a matter of terraforming the El Nido Archepelago so that, at a calculated time, causing a dimensional split would be possible. That said, orchestrating the event would be, in my opinion, the tricky part. So here's how I think it could have possibly went down.
Unless a dimensional split occurs, most 'discarded' timelines end up in the DBT. This would be the case of the events in Radical Dreamers. Given the case, Schala would have been able to see these events thus giving her not only a reason to create a clone of herself but a connection to Serge as well. This could be why Schala attempted to somehow save Serge.
How does Belthasar play into this? If he kept in contact with Lucca, he would have learned about Kid and as smart as he is, deduced that Schala had created her as part of a plan to save herself. Indeed, Project Kid could have easily been designed for Kid herself and not Serge. It wouldn't matter to Belthasar either way. Whether it was Kid or Serge who eventually made contact with the Flame, events would have played out that would have lead to a dimensional split and the creation of the ChronoCross.
Imagine if Kid had been the one to find the Flame and become the Arbiter. FATE would have still sought her out to kill her in order to reconnect with the Flame. All Belthasar would have to do then is go back in time, save her, and the dimensional split would be created. He would have then directed her on her journey to create the ChronoCross and save Schala. Instead, Schala chose Serge to become the Arbiter (intentionally or not is open to debate) and events played out as they did in the game. (Side note: Reaching Chronopolis, overcoming its defenses and coming into contact with the Flame would have been easy enough for Kid given that she was protected by that conundrum of an amulet she posessed. It wouldn't have been a breeze, but possible.)
Why was the future doomed if Serge had lived? Simple enough really. Had Serge lived, Project Kid wouldn't be able to reach a conclusion. The Time Devourer would have matured and then game over. One could almost say that Serge was destined to die once becoming the Arbiter.
As long winded as all that was, its my two cents on the whole thing.
