Degeneration conjecture for Chow-weight spectral sequences

Let $S$ be a reasonable scheme, let $M\in \operatorname{Obj}DM_c(S)$, and let $T_{w_{Chow}}({\mathcal{H}}^{et}_{{\mathbb{Q}_l}},M)$ denote the Chow-weight spectral sequence associated with $M$ and the étale realization functor.

Degeneration conjecture. The spectral sequence $T_{w_{Chow}}({\mathcal{H}}^{et}_{{\mathbb{Q}_l}},M)$ degenerates at $E_2$ for any $M\in \operatorname{Obj}DM_c(S)$.

Such degeneration would provide strong structural information about the Chow-weight spectral sequences arising from étale realizations of motives. The source gives no resolution status for this conjecture.