Enough torsion-free objects conjecture for universal Nori motives

Let $X$ be an algebraic variety over $\mathbb{Q}$. An object $M$ of the abelian category $\mathcal{M}_\mathrm{univ}(X,\mathbb{Z})$ is torsion-free if multiplication by every nonzero integer is a monomorphism. Enough torsion-free objects conjecture. For every $M$ in $\mathcal{M}_\mathrm{univ}(X,\mathbb{Z})$, there exists an epimorphism

$$N\twoheadrightarrow M$$

in $\mathcal{M}_\mathrm{univ}(X,\mathbb{Z})$ with $N$ torsion-free. This would provide the missing integral categorical input needed to upgrade the known rational equivalence and equivalence on $n$-torsion objects to an integral equivalence with perverse motives; the source presents this as a reachable conjecture, with the full equivalence still unresolved.