Revstack fertility monotonicity conjecture

Let $\operatorname{revstack}=s\circ\operatorname{rev}$, where $s$ is the stack-sorting map and $\operatorname{rev}$ reverses a permutation. For a permutation $\sigma\in S_n$, let $\operatorname{revstack}^{-1}(\sigma)$ denote its set of preimages under $\operatorname{revstack}$. Revstack fertility monotonicity conjecture. For every permutation $\sigma\in S_n$,

$$|\operatorname{revstack}^{-1}(\sigma)|\leq|\operatorname{revstack}^{-1}(\operatorname{revstack}(\sigma))|,$$

with equality if and only if $\sigma=123\cdots n$. The source presents this as an open conjecture related to fertility monotonicity.