When does construing $M$ as a simultaneous mediator and moderator of a variable's effect make sense?

Hayes (2018) p. 540 writes

I will not take a firm position on whether construing $$M$$ as a simultaneous mediator and moderator of a variable’s effect could ever make substantive or theoretical sense. I am uncomfortable categorically ruling out the possibility that $$M$$ could be a moderator just because it is correlated with $$X$$. My guess is that there are many real-life processes in which things caused by $$X$$ also influence the size of the effect of $$X$$ on $$Y$$ measured well after $$X$$. But $$M$$ would have to be causally prior to $$Y$$ in order for this to be possible, implying that $$M$$ could also be construed as a mediator if $$M$$ is caused in part by $$X$$ but also influences $$Y$$ in some fashion.

Hayes is referring to a situation like the one depicted on p. 539, i.e. a conditional process model in which $$X$$ moderates its own indirect effect. The top diagram he describes as conceptual and the bottom one as statistical.

The model would translate into the following equations

$$M = i_M = a_X + e_M$$

$$Y = i_Y + c'_1X + bM + c'_2XM + e_Y$$

It follows that the direct effect of $$X$$ in this model would not be $$c'_1$$ but rather $$c'_1 + c'_2M$$. So long as $$c'_2M \neq 0$$, $$M$$ moderates $$X$$'s direct effect on $$Y$$.

Unlike this question, I am not asking whether it can be done mathematically - I am aware that it can. Instead, I am asking: under what circumstances it will be sensible theoretically/substantively interpretable? Also, why has this question proved a controversial one in the mediation literature?

Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. Guilford publications.