Polynomial point-count conjecture for moduli spaces of smooth curves

Let $\mathcal{M}_{g,n}$ be the moduli space of smooth curves of genus $g$ with $n$ marked points. Polynomial point-count conjecture. The space $\mathcal{M}_{g,n}$ has polynomial point count if and only if

$$3g+2n<25.$$

The known implication in the range $3g+2n<25$ follows from Tate-type cohomology results, while the source says that polynomial point counts are expected to fail outside this range; no general proof of the converse is given.