Problem there, Killercactus, is that letting Serge live destorys the future somehow (the exact process is never stated, but if Serge lives past 1010, the future's crap).
I don't think we know this for sure. We know that if Serge lives past 1010
as an Arbiter of the Frozen Flame, the future's crap. The exact process is never stated, but I've always assumed it had to do with the plotline that didn't totally make it into Cross, about Serge being consumed by the TD since he is an Arbiter. If he never becomes an Arbiter, the future may be safe after all - there's just no way to save Schala.
And you're right - Belthasar's first priority was to save Schala, for which he needed a Chrono Cross. To get a Chrono Cross, he needed two dimensions that had a Dragon Tear in them. The thing is though, there were already two dimensions with a Dragon Tear (Another World and the Radical Dreamers dimension), but he didn't have anyone that could traverse them (possibly besides FATE, but FATE has no need for it). What he needed was someone that could traverse two dimensions and obtain two Dragon Tears to create a Chrono Cross. He then probably decided just to use this person to defeat the TD as well, since the person would need to fight through hell just to create a Chrono Cross.
So, in order to make a dimensional-traveler, he knows he needs that person to touch the Flame. He installs Prometheus so that when that happens, FATE will challenge this person enough to be empowered by the end of the journey, and also to originally kill the person so that Kid can change the past and split the dimensions (he may also know that FATE will obtain one or both Dragon Tears to try and override Prometheus). In order to have that person touch the Flame, he needs to shut down Chronopolis' defenses. In order to do that, he needs Schala's power. In order to get Schala's power, he has to find someone she believes is worth saving, and the only available option to Schala to save that person must be the Flame.
So, if he observes the RD dimension in which Serge is not attacked and not made an Arbiter, and notices Kid and Serge's possible romantic attraction, he could decide that Schala would believe Serge is worth saving by using the Frozen Flame. That could be why Serge is chosen for all of this in the first place, and Belthasar could have set the panther demon on him to begin all of this.