Vanishing conjecture for the top cohomology of mapping class groups

Let $\operatorname{Mod}_g$ be the mapping class group of a closed, oriented surface of genus $g\geq 2$, and let $H^*(-;\mathbb{Q})$ denote rational group cohomology. Vanishing conjecture. For each $i\geq 0$ we have $H^{4g-5-i}(\operatorname{Mod}_g;\mathbb{Q})=0$ for $g\gg i$. This is presented as the vanishing consequence of the proposed stable instability for mapping class groups; the source gives no resolution of the general statement.