Simple connectivity of limits of universal covers of RCD spaces

Let $(X_i,d_i,\mathfrak{m}_i)$ be a sequence of $RCD^{\ast}(K,N;D)$ spaces, and let $(\widetilde{X}_i,\widetilde{d}_i,\widetilde{\mathfrak{m}}_i)$ be their universal covers. Assume that these universal covers converge in the pointed measured Gromov–Hausdorff sense to an $RCD^{\ast}(K,N)$ space $(X,d,\mathfrak{m})$. Universal-cover limit conjecture. The limit space $(X,d,\mathfrak{m})$ is simply connected. The question concerns stability of simple connectivity, or equivalently of the universal-cover structure, under pointed measured Gromov–Hausdorff limits; the source states it as an open problem.