Quotient-freeness conjecture for relational wiring-diagram algebras

Let $\mathcal{S}$ be the singly typed wiring diagrams operad. For a set $A\in\operatorname{Ob}({\bf Set})$, let $\mathcal{R}\textnormal{el}_A\in\operatorname{Ob}(\mathcal{S}\text{--}{\bf Alg})$ be the relational algebra of type $A$. An algebra $R$ is quotient-free if, for every other $\mathcal{S}$-algebra $P$ and epimorphism $f\colon R\rightarrow P$, either $f$ is an isomorphism or $P$ is isomorphic to the terminal algebra $\{*\}^{\mathcal{S}}$. Quotient-freeness conjecture. The relational algebra $\mathcal{R}\textnormal{el}_A$ is quotient-free.