Torsion characterization by stable torsion length

Let $\operatorname{Mod}_g$ be the mapping class group of a closed orientable surface of genus $g$. For $f\in\operatorname{Mod}_g$, let $\tau_g(f)$ be the minimum number of torsion elements whose product is $f$, and define the stable torsion length by

$$||f||_{\tau_g}=\lim_{n\to\infty}\frac{\tau_g(f^n)}{n}.$$

Stable torsion length conjecture. If

$$||f||_{\tau_g}=0,$$

then $f$ is torsion. This is presented as a stronger version of the conjecture on Dehn twists. The source notes that torsion elements have stable torsion length zero, but gives no resolution of the converse.