I think this would work nicely. I'd been thinking about the bark as well, and had come up with the idea of making fires take kindling when you go to start them up. Larger pieces of wood, and even coal/charcoal, are difficult to get burning without something smaller or a lighter fluid.
So, I'd say this, and add in the idea that bark, branches, and torches can serve as kindling. (This will also highly increase the value of keeping a fire going at a workstation, rather than turning it on and off repeatedly.)