Worst-case identifiability conjecture for general coalescents

Let $\Xi\in\mathcal{X}$ be the finite measure governing a general $\Xi$-coalescent, and let $\psi^\Xi_n$ denote the quantity controlling the additional sample-size requirement for identifiability of the expected site frequency spectrum. Identifiability conjecture. For all $\Xi\in\mathcal{X}$ and $n\geq 3$,

$$\psi^\Xi_n\leq\left\lfloor\frac{n-1}{2}\right\rfloor-1.$$

The conjecture asserts that the point-mass coalescent with mass at $1/2$ gives the worst case for identifiability among the considered $\Xi$-coalescents. If true, it would provide a uniform upper bound on the sample-size correction needed to identify the demographic history from the expected site frequency spectrum; the supplied text gives no resolution.