"They have better things to do. But don't worry mortals, you'll be gotten to eventually."
And now back to OOC...
Most of the fiends that can make the transit to the Prime by themselves, generally do have more pressing things to worry about on the planes. Typically it's more damaging to them to just abandon those commitments, be they to the Blood War, or internal struggles in the Abyss, Baator, Gray Waste, Gehenna, or Carceri. Sure it might be fun for a Pit Fiend to abandon his post in Baator or as a marshal of a pack of a hundred thousand barbazu marching across Oinos, all for what amounts to a free buffet on prime material world X, but he'll probably be demoted to lemure status for that little stunt.
For fiends that can't make the transit on their own, they probably have less to risk if they do manage to find a stable portal, or end up being summoned and slipping their bonds. They'll have fun before they get shunted back to their native plane certainly.
Of course, sometimes the Blood War itself spills over onto the prime, probably just as often by horrific accident than by intent. When it does, it normally ends up sterilizing that world completely and probably adding some new real estate drifting in the Astral, IYKWIMAITYD, or at the least leaving it a burned out, ravaged husk that will never be the same.