Okay, I've read so much screed on the subject that I've lost sight of the true dark of the matter. And I've skimmed most of my 2e Planescape collection without success. So, if somebody could please answer this question for me and site a 2e source, I would be very appreciative indeed.
Why don't the fiends (or any of the other exemplars, for that matter) overrun the Prime? Aside from them fearing the deities, which they fear on the Outer Planes just as much, there is a great reason to do so. After all, the beliefs of the primes fuel the life and nature of the outsiders. Why, then, isn't the Prime a free-for-all battleground for all the exemplars of the Great Ring? Faces of Evil: The Fiends says that the Baatezu sometimes make arbitrary rules concerning how many of them can visit the prime, but aside from that, both they and the Tanar'ri can freely romp the Prime. I know there's a reason they don't... I remember something... I just can't recall what it is and where I read it.
Among other things:
1) fearing the deities ain't chicken feed. ;^) Any effort fiends put into propagandizing on the Prime will be countered by the servants of the Uppler Planar deities, who can be a lot more straightforward about their aims. People like angels and don't like demons; it would be an awful lot of effort to change that view, and you'd have to convince some real high-ups that it would be profitable.
2) Blood War takes up a lot of time and effort.
3) Thing about exemplars on the Prime is, they aren't natural there -- they can be banished, and fiends often are. Fewer people go around wanting to banish angels, but for various reasons good gods seem to want to leave human free will as intact as possible and not send their nonhuman servants to meddle in human affairs every day. (Pick your reason: they don't have the energies, familiarity breeds contempt, treaty among Powers, etc.)
This is all off the top of my head, but I imagine the main thing is that exemplars on the Prime can be banished -- by other exemplars running around the Prime, too, so for the most part it would be a lot of effort canceling each other out.