I had never thought that FATE was the one who destroyed the Dead Sea. I had always thought that Miguel, being alive in that dimensional distortion, held it together simply by being alive since he was the Guardian of the Dead Sea appointed by FATE.
(after several minutes of watching a Chrono Cross youtube.com video clip...)
Now I see why I always thought that the Dead Sea would cease to exist if Miguel died, it happens to say so, directly quoted from the game;
"Miguel:Wouldn't you all like to become one with this world?
-To be part of Eternity? How about it, Serge?
-You need no longer to struggle alone, nor fear an uncertain tomorrow.
-Well? What do you say?
(At this point you have the option of choosing 'Refuse!!!' or 'Accept...', which if I remember if you pick accept, your party members try to talk you out of it.)
Miguel:I see... I guess there's only one thing left to do then...
-I take it you're trying to restore the dimensional distortion?
-If you defeat me and liberate this place, the distortion will return to the way it was.
-I guess this is it... Just as there are times of peace, there are times of war...
-You don't have to hold back. Attack me with all your soul if you wish to live.
-Let fate take its course...!!!"
...After the battle everything starts to shake, it does confirm that FATE does indeed want and will destroy the Dead Sea with Serge and Co. in it. But the thing that's said immediately after everything starts to shake;
"Miguel:It looks like Fate has made its decision and has started to carry it now..."
Notice that he said 'Fate', not 'FATE', in that sentence. The whole Dead Sea disappearing just seems to me that it's a natural result of Miguel dying, he is the guardian of that place, not FATE(because FATE is in Another World), meaning that while Miguel is alive, he is keeping the Dead Sea existant. The Dead Sea is the keeper of the Frozen Flame in Home World, in this case FATE doesn't have access to, which Miguel explains why FATE will destroy the Dead Sea.
Anyhow, I believe two things were occurring during the cutscene, one of them, are those 3 flaming lines directed at the Tower of Geddon, which has been discussed as that being the action of FATE. And the other, that white light shooting at the sky. I don't know about you, but that doesn't seem like FATE's doing, more like the natural course of the Dead Sea about to be corrected(disappear to the Darkness Beyond Time) because there is no guardian to keep it existing.
This is how I see it. Miguel does mention that FATE predetermined everything that Serge and Co. would do and eventually arrive and meet up with Miguel at the Tower of Geddon. Lynx would have Serge's body and able FATE to access the Frozen Flame. FATE chose Miguel(because of his prowess, since to first timers he seems to kick your butt over and over) to become the guardian of the Dead Sea as FATE was not able to guard it itself, not being present in Home World. FATE wants Serge to die in the Dead Sea, so why wait until after Serge defeats Miguel? I believe FATE predetermined that Miguel would defeat Serge, should the two of them meet and do battle, FATE would have not worry about the Home World Frozen Flame to be accessed by another party than its own. Miguel seemed to have also thought that Serge would not be able to best him in combat and seemed to already accept the situation as it was. But when Serge defeats Miguel, his sight on things seemed to have shifted for the better of things, because let's face it, after the Dead Sea scenario, Serge and Co. just seems to straight out defy fate and destiny throughout the rest of the game, even the Sky Dragon seemed to be surprised by the turn of events and FATE just seemed to be in a state of panic towards Serge from the entire time that you actually see FATE in the game.
I also do believe that light that comes from the Tower of Geddon, was supposed to be the Home World's Frozen Flame about to reveal itself to Serge after Miguel was defeated. But of course it seems to be destoryed by FATE after the 3 flaming lines collide with the light as it results in that explosion that just plains wrecks all of the buildings and frozen water in the Dead Sea. Afterwards, there is an implosion, the energy of the explosion and the clouds in the sky gets sucked into a condensed white ball and thrown into the Darkness Beyond Time as Miguel said so himself.
After that explanation, I believe that FATE destroyed the Dead Sea, but did not make it disappear to the DBT, that effect was more from the defeat of Miguel. Kinda makes FATE's move on destroying the Dead Sea a little irrelevant since it was about to disappear anyway, perhaps that was just a method of hasting that effect and hopefully, in FATE's favor, would force Serge out of the scene for good.
Oh geez, I've been working on this for 3 hours and it's now 4AM. I apologize if any of my explanations hardly made any sense, I'm tired, let alone talking about time travel and dimensions is enough to make anyone easily falter in their theories.