Descent and generalized Whittaker wavefront set conjecture

Let $F$ be a local field of characteristic zero, let $G$ be a classical group over $F$, and let $\pi\in\Pi_F(G)$ have a generic local $L$-parameter. Let $\operatorname{WF}_{\mathrm{des}}(\pi)$ be the descent wavefront set and let $\operatorname{WF}_{\mathrm{wm}}(\pi)$ be the generalized-Whittaker wavefront set. For $\square\in\\{\mathrm{des},\mathrm{wm}\\}$, use the superscripts $s-\mathrm{max}$ and $r-\mathrm{max}$ for maximal members under the $F$-stable and $F$-rational topological orders, respectively. Descent and generalized Whittaker conjecture. One has

$$\operatorname{WF}_{\mathrm{des}}(\pi)^{s-\mathrm{max}}=\operatorname{WF}_{\mathrm{wm}}(\pi)^{s-\mathrm{max}},\qquad \operatorname{WF}_{\mathrm{des}}(\pi)^{r-\mathrm{max}}=\operatorname{WF}_{\mathrm{wm}}(\pi)^{r-\mathrm{max}}.$$

The proven inclusion of the descent wavefront set in the generalized-Whittaker wavefront set motivates this conjecture, which would identify their maximal members for both orders.