Mobility conjecture for complete intersection curve classes

Let $X$ be a smooth projective variety of dimension $n$, and let $A$ be an ample divisor on $X$.

Mobility conjecture.

$$\operatorname{mob}(A^{n-1})=A^n.$$

This conjectural description of the mobility of a complete intersection class would imply that the mobility of every pseudo-effective curve class agrees with its volume, completing the equality in the main theorem. The statement is attributed to Question 7.1 of Lehmann's work.