Apparently, the loss of a homeworld isn't as big a threat as the constant worries over Earth would have us think.
With something like the Federation, Klingon or Rihansu Empires etc, enough of a population has spread out to prevent extinction and provide resources to stave off climatiological collapse.
Qo'Nos certainly has a much more bleak atmosphere with Klingons huddled inside a lot more than the beautiful blue version in Enterprise where they were frequently outdoors, so it did have some effect.
I think they were panicking over it more than they should have been in TUC, and Gorkin used it to his adventage to push for peace. Probably why Chang did what he did, knowing he could sabotage the peace talks and still have a powerful enough Empire by the time the dust settled.