Stable b-infinite transitivity conjecture for unirational varieties

Let $X$ be a unirational algebraic variety over a field $\mathbf{k}$. The field $\mathbf{k}(X)(y_1,\ldots,y_m)$ is said to admit an infinitely transitive model if it has a model that is infinitely transitive, where infinitely transitive means that the subgroup of $\operatorname{Aut}(X)$ generated by additive-group actions acts transitively on every finite ordered collection of points. A variety is stably b-infinitely transitive if such a model exists for $\mathbf{k}(X)(y_1,\ldots,y_m)$ for some $m\geq 0$ and $\mathbf{k}(X)$-transcendental elements $y_i$. Stable b-infinite transitivity conjecture. Any unirational variety $X$ is stably b-infinitely transitive. This would connect unirationality with the existence of models admitting highly transitive unipotent group actions, extending the known fact that rational varieties are stably b-infinitely transitive. The source provides no resolution, so the conjecture remains open.