This question is about the [article](https://arxiv.org/abs/2211.06120) "Motivic local systems on curves and Maeda's conjecture" by Yeuk Hay Joshua Lam.

In the proof of Theorem 1.1 it is claimed (on lines 4-5 of p. 7) that any motivic local system of rank $2$ (on a curve) with infinite monodromy must be a direct factor of a family of abelian varieties $p : \mathcal{A} \to X$. (By this I think the author means that it should be a direct factor of $R^1 p_* (\mathbb{C}_{\mathcal{A}})$.)

No reason is given for this claim and I'd be grateful for an explanation (or any other comments/suggestions). In Theorem 1.1 the local system is in fact an $\mathrm{SL}_2$-local system and this assumption might be needed for the statement to be true.