Polynomial-count conjecture for character varieties of split reductive groups

Let $G$ be a split reductive algebraic $\mathbb{C}$-group, and let $\mathfrak{X}_r(G)$ denote the character variety of a free group of rank $r$ in $G$. Polynomial-count conjecture. The variety $\mathfrak{X}_r(G)$ is polynomial-count. This would extend the polynomial-count phenomenon established in the paper for the considered special linear character varieties to arbitrary split reductive algebraic complex groups; the source gives no resolution.