The folklore conjecture on first-order model checking in interpretations of bounded-expansion classes

Let $\mathcal{G}$ be a graph class with bounded expansion, let $I$ be a simple first-order graph interpretation scheme, and let $\varphi$ be a first-order property to be tested. The interpretation $I(\mathcal{G})$ consists of the graphs obtained by applying $I$ to graphs in $\mathcal{G}$. Folklore conjecture. First-order model checking is fixed-parameter tractable on $I(\mathcal{G})$, parameterized by $\mathcal{G}$, the interpretation scheme $I$, and the first-order property $\varphi$ to be tested. This conjecture concerns the tractability of first-order model checking for graph classes that may be dense but are structurally derived from sparse classes. It remains open in the stated generality.