Microtubules polymerize from identical tubulin heterodimers, which form a helical lattice pattern that is the microtubule. This pattern always has left-handed chirality, but it is not known why. But as tubulin, similar to other proteins, evolved for a purpose, the question of the title of this artcile appears to be meaningful. In a computer simulation that explores the 'counterfactual biology' of microtubules without helicity, we demonstrate that these have the same mechanical properties as Nature's microtubules with helicity. Thus only a dynamical reason for helicity is left as potential explanation. We find that helicity solves 'the problem of the blind mason', i.e. how to correctly build a structure, guided only by the shape of the bricks. This answer in turn raises some new questions for researchers to address.