March 2018 Update: Even though this had been requested on Meta Stack Exchange five years before it was posted here (thanks to Zanna for finding that), in the intervening 8+ years it has never gotten much attention. As of this writing, that MSE question only has about a hundred views. I still do very much hope that this feature gets implemented! For the time being, Zanna has written a SEDE query that anyone can use to find all their merged answers (or all the merged answers of any other specific user).
This is a good idea, because:
There's no disadvantage to notifying people that their answers have been migrated. (See below for one theoretical disadvantage, and why it's not really a disadvantage.)
Sometimes an answer should be edited or removed, or the question should itself be edited to make it more general. Notifying authors of answers can help make this happen.
The system's current behavior is not entirely consistent with our values vis a vis the treatment of authors.
When one user creates a post and another user edits it, it's made clear that the current version of the post is not just created by the original author. Therefore, we are not "putting words in people's mouths." That is, we are not making it look like people said something they have not said. This is good.
But when an answer is migrated, the context in which its author said it is changed, usually without any obvious indication of the change. In effect, we run the risk of making it look like people have said something they have not said. This is bad.
I am not saying that we're violating anyone's legal rights by merging silently. I suspect we are not, though I really have no idea and I am not a laywer and this is not a legal argument. But we are doing something that another website would not be allowed to do, or at least which we do not want other websites to be allowed to do. We're publishing someone's post somewhere else, without providing a link to where it was originally published. We're republishing people's work, out of context.
To reiterate, this is not a legal argument. Instead, it is an ethical one (and an argument about how to make the site work more smoothly). Since we don't provide links over/under merged posts to the question where they were originally posted, we should at least notify their authors so they can make any clarifying changes they think are appropriate.
With all that said, please note that most of the time, when a post is merged, its author shouldn't have to do anything. If a post's author has to do something to make a merged answer make sense, that suggests that moderators may have made a mistake in doing the merge, in the first place.
So long as this feature doesn't lead to dissimilar questions being merged more often--which it doesn't have to, we can use the same guidelines we use now--I see it as only positive. It's hard for me to imagine a situation where an author would not want a notification that their work had been moved from one place to another.
