They might not be able to safely leave the End of Time. There's only one gate key.
Sorry, but I'm gonna have to invalidate that one. Remember, in one of the endings, everyone goes their seperate ways <i>without</i> Gate Keys.(Well, except Marle and Lucca.) So the portals at The End of Time, for some inexplicable reason, work just fine with or without a Gate Key.
In any case, this is an interesting question. I can give you a couple of theoretical explainations:
[Gameplay Explaination]No Time Key, no character transfers. No character transfers, no way to contact the other party members. As such, you're incapable of playing as anyone else.
[Story Explaination]Gaspar sleeps a lot, seeing as he has nothing better to do since being at The End of Time. Though not quite as gifted as Belthesar(apparently), he may very well have known about everything that would happen. But then again, he may very well have
not known. Given all this, the other members would have no reason to worry more than normal and have no information to go on besides. In addition, the Wings of Time(or "Epoch") was stuck on board the Blackbird. Even if the others
had taken the Time Gate back to 12,000 BC, they would've been stuck there with no Gate Key and with no way to get aboard the Blackbird until the first party managed to break...which would have defeated the purpose of going back in the first place!
In summation, Gaspar, even if he'd known about this stuff happening, would have had no good reason to tell anyone to go back to 12,000 BC because without a way to get on to the Blackbird, anyone else going back would have just been a waste of time.
Conundrum solved!