But then, variety is considered to be important to a lot of raw feeders. Anyone know why?
Gut flora will become limited if you consistently feed only a limited number of things. It is for this reason that a dog on kibble alone will get sick if you suddenly switch the food, because the good bacteria in the gut isn't accustomed to that new stuff. People are the same...I have a terribly sensitive digestive system and if I eat something completely new, I tend to get really sick for a while. Eating greasy, fatty meats after many months of rabbit or venison only left me REALLY unhappy the other day. Trust me, it wasn't amazing.
A varied diet is also preferred for raw or natural feeding because in nature, wild canids eat a very diverse ammount of foods. Cats are true/strict carnivores, but dogs are actually somewhat omnivorous. Mirroring a wild and varied diet is the goal of a lot of holistic or natural food enthusiasts.
I personally have considered semi-raw cooked diets for my pets...but the cats who need it won't eat anything but kibble (gods how I've tried to get them to eat something, ANYTHING else!!!!) and the dogs don't hold weight well on it and I don't like them to be too thin (not the fault of the recipes either, my one dog has serious issues). So for now, I feed a high-quality kibble.
but if you feed whole, shouldn't it be OK to feed mainly rabbits? Feeding whole will help the Omega 3:6 balance, which benefits the coat/skin a lot...
In a word, no. There's no hidden fat on a rabbit that will keep your dog healthy. If you do not feed other sources of fat, as well as carbohydrates and allsuch, your dog will become nutritionally DEFICIENT. Remember that dogs are semi-omnivorous?
One protein source is a bad plan for feeding raw or BARF diets.