back in my MTB days (before i moved from the jungle of CT to the ... urban... jungle? of NYC) I had a completely F***ed rear wheel with a lousy brake which was impossible to adjust correctly. On the front, though, i had a nice Avid disc brake. I don't think it would be an exaggeration to say that i never used the rear brake, no matter how steep, how rocky or rooted the trail was.
Of course, my front brake was a disc brake. If you have a weak front brake, you probably need a rear brake to compensate to some degree or another.