The extremal ML degree bound for graphical models

Let $G$ be a graph. Write ${\rm eMLD}(G)$ for its extremal maximum likelihood degree and ${\rm MLD}(G)$ for its Gaussian maximum likelihood degree.

Extremal ML degree bound. For any graph $G$,

$${\rm eMLD}(G) \leq {\rm MLD}(G).$$

The equality for suspension graphs motivates this proposed upper bound, but the conjecture is not resolved in the supplied text.