Monotonicity of maximum likelihood degree under facial submatrices

Let $A \in \mathbb{Z}^{n \times r}$ and $\overline{A} \in \mathbb{Z}^{n \times s}$ be a facial submatrix of $A$. The facial-submatrix maximum likelihood degree conjecture. The maximum likelihood degree of $\mathcal{M}_A$ is greater than or equal to the maximum likelihood degree of $\mathcal{M}_{\overline{A}}$. This would extend the preceding theorem on maximum likelihood estimators for facial subsets and express monotonicity of maximum likelihood degree under passage to a facial submatrix; the source does not provide a proof or resolution.