Kuja was a master of spreading fear and panic.

First it was his Black Mages spreading death everywhere they went. They were known and spoken about with terror across the continent.

Then later on he brings the Mist back which covers the entire world, causing various deaths by the Iifa Tree's roots ripping up through the ground. The heavy concentration of Mist also produced new and harder monsters.

Though the fall of Shinra, due entirely to Cloud's group, had a profound impact on FFVII Gaia.

Though, it wasn't entirely their doing. Diamond WEAPON "killing" Rufus helped. But Cloud and the gang stamped out the rest of the heads.

But I'm sure people in the other worlds would be just as hopeless and depressed as those in FF7 if they saw death approaching them day after day.

No one in FFIX knew they were gonna die except the party.

I may be wrong but didnt Ulti achieve time compression at the whim of the main characters
Yes. She was too weak to go back in time and needed the heroes to help her and use the Plot Device Ellione.