My book talks about it, but doesn't give a very intuitive reason why. It essentially says that from a modified version of Liouville's Theorem, the electrons in a band stay in that band. Then it says the phase space (position-wavevector phase space) has a constant density through time, and if that's the case, when you calculate the electric and energy current densities, you sum over the Brillouin zone, and each of these currents somehow come out to zero. I believe them well enough I guess, but I'm looking for a more intuitive explanation. Can anyone direct me to one?