I would say yes, there are cases in which I have thought that this would be a nice thing to have. Especially when cross-posting to a smaller niche community.

I can think of a few potential small issues. For example, cross-posters can edit the body of the message, so you might in some cases end up with comments that seem out of place as they refer to the content specific to a cross-post. You also have the rare case in which the same post might mean different things in different communities.

But, overall, I see it as beneficial. Quirks can be fine-tuned later on.