Because when the original Cocoon crashed into Pulse, Pulse would be inhabitable for an extended period of time, kind of like if a chunk of an asteroid crashed into Earth, or a major nuclear event took place. That's how I interpreted it all from the way things looked in Noel's time, anyway.

There's also the whole matter of all those giant Pulsiean monsters running around that living on Cocoon would negate. You have to remember that even though people managed to build cities on Pulse, humans hadn't been living on Pulse and having to deal with Pulse's conditions for centuries, so they weren't exactly accustomed to it.

Then again, we are talking about a game where giant flying mechs equipped with arsenals of guns and canons are being fought off with swords, boomerangs and staffs and the guy with a machine gun readily available is fighting off the other guys with machine guns via his fists, so I see no need to split hairs on the matter.