Do we need this as a separate option now that we have vertex color display support? We don't generally do this for modifiers that generate some kind of data. You could argue the same should exist for vertex group or uv mapping modifiers, but then it becomes too much.

Hi. I have no opinion about whether this is better as a new overlay option or from existing Vertex color option. What I am not sure about is how it would be better for the user, where it allows him to easily realize what he must do to be able to see Dynamic Paint result in solid mode. You remember that in 2.79 this works immediately by default without user intervention, even without having added a Vertex Color layer in the Object Data tab.
Edit:
Is this about workbench Dynamic Paint visualization, right? If it is not, sorry for the misinterpretation and you can delete this comment.

I'm not opposed to some generic system to easily visualize data layers from a modifier. But adding a specific Dynamic Paint setting in the overlay settings seems like the wrong direction to me, and either way I would not think this is high priority.