Conjecture that torsion has density zero in the mapping class group

For a fixed finite generating set of ${\rm Mod}_g$, define the density of a subset $S$ by

$$d(S)=\lim_{r\to\infty}\frac{\#(B(r)\cap S)}{\#B(r)}.$$

Let $\Tor_g$ denote the set of finite-order elements of ${\rm Mod}_g$. Torsion-density conjecture.

$$d(\Tor_g)=0.$$

This is presented as a further test related to the conjectured density-one prevalence of pseudo-Anosovs; the source gives no resolution.