To be fair, any story involving time travel is destined to have so many holes. The weird thing is that this hole has nothing to do with time travel.
I imagine that regardless of the fact that there are flying fal'Cie and whatnot, Cocoon could easily be simply too high for the vast majority - if not all - of fal'Cie/dragons/etc. to reach. And if you're going to defend against something, it's generally easier to defend against a handful of dragons than a handful of dragons and a countless number of land-dwelling beasts. I still think there could be justification for making a new Cocoon on those grounds. I'm not saying there is justification, but if there was any, that would probably be it.
The problem is that they never bothered to tell us in-game what that justification was. The moment they discussed making a new Cocoon, they should have immediately told us why.
Also, was the old Cocoon still inhabited to any major degree? I can't remember any locations we went to that were actually on it.