For me what is fundamentally important about composting (and by the definitions I've been using, "sheet mulching" as described up-thread is a form of composting) is returning biomass to the soil, instead of digging it out, scraping it off, bagging it up and hauling it away somewhere such as usually a landfill where it is of no use to the earth or anybody.
However it's done is fine with me! and IMO it's a matter of finding the method that works for the situation one is in. Where I live? I kind of doubt sheet mulching would work very well. Plus, here, the pre-existing practices have removed so much of the organic matter over time, adding it back in however we can is a primary goal of mine.
I've used uncomposted rabbit poop just fine and also heard from others both stories: it burns, and, it doesn't ever burn. Maybe it's a matter of what the rabbits eat?
Humans and most dogs and cats eat things that make the manure pretty unpleasant to deal with, even compared with raw chicken manure which as we all probably know is pretty strong smelling. I've been taught that the bacteria in human and dog and cat manure is the big problem with using them in compost; however, of course traditional ag systems have used "nightsoil" for eons. Those folks didn't have artificial chemical additives, preservatives, colors and flavors added to their food, and that may make a difference too.
