Free rational curves in the smooth locus of klt Fano varieties

Let $(X,\Delta)$ be a klt Fano pair over an algebraically closed field of characteristic $0$. A rational curve in $X$ is free when its pullback tangent bundle is nef. Free-curve conjecture. There is a free rational curve in the smooth locus of $X$. This conjecture is motivated by work of Keel–McKernan and Miyanishi–Tsunoda; the paper proves the assertion in the settings covered by its results, but the supplied context does not establish whether this exact characteristic-zero statement is fully resolved.