Notice that cleavage has nothing to do with imperfections in the crystal. Indeed, if you try cleaving an imperfect crystal, you may find that it cannot be cleaved as well as a perfect one. The cleavage is the result of the orderliness of the atomic arrangement. No wonder imperfections, which disturb the orderliness, disturb the cleavage as well. You will also note that the cleavage directions are obedient to the symmetry of the crystal.