The power-integral Cohen–Macaulay conjecture for affine toric varieties

Let $\kappa$ be a field, let $X\subset\mathbb A^n_{\kappa}$ be an affine toric variety, and let $A$ be its coordinate ring. Let $A^{\operatorname{pow}}$ denote the ring of power-integral elements of $A$.

Power-integral Cohen–Macaulay conjecture. The ring $A^{\operatorname{pow}}$ is Cohen–Macaulay.

This is proposed as a version of Hochster's Cohen–Macaulayness theorem for affine toric rings, yielding a potentially smaller MCM than the normalization. It is open in the stated generality.