The visibility conjecture for prime ideals in tensor-category algebras

Let $k$ be an algebraically closed field, let $\mathcal{C}$ be a tensor category of moderate growth, and let $A\in\mathsf{Alg}\mathcal{C}$ be an algebra object. A prime ideal $\mathfrak{p}\in\operatorname{Spec}A$ is visible if it is the kernel of an algebra morphism $A\to S$ to a simple algebra $S$. Visibility conjecture. Every prime ideal in every algebra object $A\in\mathsf{Alg}\mathcal{C}$ is visible. Visibility would extend the classical correspondence between prime ideals and maps to simple residue-type algebras to the setting of tensor categories; the source gives no resolution status.