Finiteness conjecture for crepant-birational fibres of maximal-variation fibrations

Let $X$ be a $\mathbb{Q}$-factorial variety, and let $f\colon(X,\Delta)\to Y$ be a klt-trivial fibration of maximal variation. Write $\Delta^h$ for the horizontal part of $\Delta$.

Finiteness conjecture. There is an open set $U\subseteq Y$ such that for every $y\in U$ the set

$$\{z\in U\vert\; (f^{-1}y,\Delta^h\vert_{f^{-1}y})\; \text{is crepant birational to}\; (f^{-1}z,\Delta^h\vert_{f^{-1}z}) \}$$

is finite.

This expected finiteness property links maximal variation with the birational moduli of the fibres. The source presents it as conjectural and does not state a general proof.