Dao and Takahashi's infinite-radius conjecture for resolving subcategories

Let $R$ be a Cohen--Macaulay local ring, and let $\mathcal{X}$ be a resolving subcategory of $\operatorname{mod} R$. A module is maximal Cohen--Macaulay if its depth equals $\operatorname{dim} R$; call it non-MCM when it is not maximal Cohen--Macaulay. Dao and Takahashi's conjecture. If $\mathcal{X}$ contains a non-MCM module $M$, then $\mathcal{X}$ has infinite radius. This conjecture extends Dao and Takahashi's theorem that a resolving subcategory containing a module of positive finite projective dimension has infinite radius; the general Cohen--Macaulay case remains open.