I've also run into a lot of controversy about feeding rabbits on an "alternative" diet. But according to this person and many others, it's just as good, if not better, than feeding rabbits on a "traditional" diet of pellets and dried timothy hay. And if I pick out plants that correspond to pellets and hay, the process will be familiar and easy. High-protein vegetables can replace pellets, and high-fiber fresh grasses can replace dried hay (at least in the summer). In the winter, willow bark and dried hay can be fed.
And there is. The hay I feed my rabbits is dried Timothy grass. And fresh timothy, oats, barley, wheat, or regular ol' crab grass can be used instead of hay.
Fresh foods are also, as a rule, much higher in vitamins and minerals than dried foods. (This holds true for humans as well.) Thus, rabbits fed on fresh leafy foods are healthier than pellet-fed rabbits.