Ah ha, I found the quote that I think you are referring to:
It looks like Fate has made
its decision and has started
to carry it out now...
FATE doesn't want the Frozen
Flame to awaken in this place
at this time...
It would choose to destroy the
Flame along with the whole Dead
Sea, than to allow its enemies
to take hold of the Flame...
This lost future is about to
disappear into the darkness
beyond the dimensions again...
You have no time to spare.
You must leave here
immediately!
Quick...go!
Yeah, it seems that the "destruction" of the dead sea was entirely about the Frozen Flame.
Though, it is odd that FATE didn't want the FF to "awaken." I suppose that may just be a poetic way of saying that it didn't want anyone getting ahold of the FF and using its power before it did, but it might also refer to a sort of conciousness (and the FF does seem to have a sort of conciousness of its own).
Also, the manner in which the Frozen Flame was destroyed is curious. The Dead Sea wasn't so much destroyed as it was sent back to the Darkness Beyond Time (it came from there once, the implication then is that it could return again. And if it can return, it isn't really destroyed). Did FATE actually effect any physical aspect of the Dead Sea (and in turn, the Frozen Flame) or did it just shunt the timeline back into the DBT and close the temporal-leak-like-thingy that allowed the ruined future to manifest itself in the Dead Sea in the first place? I am asking because this might imply that it "destroyed" the Frozen Flame by sending it back to the Darkness Beyond Time.
After the Dead Sea evaporates, it isn't like the Sea of Eden returns; the curious temporal qualities of the area seem to have been largely eliminated.
However... Miguel seems to be a key to the Dimensional Distortion at Opassa Beach as well. I have no idea why killing him should restore it (which implies that Miguel somehow had the power in the first place to prevent it's use). I suppose killing Miguel might have been the event that collapsed the temporal qualities of the Dead Sea as well (why this should be so, again I have no idea).
As a side note, I can't find script confirmation that Miguel in the Dead sea is the Miguel from another world. Indeed:
Yes... I've been here
in this very place...
For 14 years...
It wasn't like this
when I got here, though...
An incident that occurred
10 years ago, transformed
it into the Dead Sea.
That seems to include that he personally was at that location when the Sea of Eden became the Dead Sea, and thus he is Home World Miguel.
However, in Chronopolis the Serge & Squad do access a computer that reveals:
However...
Ever since the formation of
the Dead Sea 10 years ago...
FATE has been unable to intervene
directly with World 01.
The best FATE could do was cross
the dimension and receive data
through the Records of Fate.
And with much difficulty, FATE
succeeded in binding Miguel
to the Dead Sea as a watchman...
I suppose one could intrepret this as that FATE crossed over with Miguel (especially if we assume that the formation of the Dead Sea would have killed Home World Miguel), but that doesn't actually claim as much. Just, that FATE binded a Miguel as a watchman (and this is probably what gave him the powers we see him display, in game).
I wonder, then, where Miguel is in Another World. Maybe FATE killed him there, as it had no use for him.
EDIT: Side note: Miguel is a variation of Michael, one of the Archangels of God. Miguel's relationship to FATE (aka, the Goddess) could be interpreted as him being an archangel as well. Some interpretations even have Michael being the one who guarded the Tree of Life after the fall (effectively, making Michael the "watchman" of a fallen Eden). Michael was also associated with healing, and Miguel was guarding the Frozen Flame (which healed Serge). In some places Michael is also the patron of Mariners. And, of course, Michael is the angel that is often depicted as standing over a defeated dragon (which represents satan). I hope I shouldn't need to explain the significance of a defeated dragon in Chrono Cross terms. Michael was also a psychopomp, and the Dead Sea could thus also be related. When individuals are faced with death, Michael supposedly comes and helps them redeem themselves (the battle with Miguel being part of Serge's motivation to find out what is going on and ultimately save the world). And Michael was the one to tell Daniel what was to happen in the future (of Israel). Miguel was the one to tell Serge and the others about the future (in the form of the dead sea).
Faust, I do quite like the idea of FATE attempting to keep the Frozen Flame from Harle, however I don't see why it couldn't be both Harle and Lynx/Serge.