When a question begins by saying "This question appeared earlier on math.stackexchange.com" and links to that earlier posting, how does it make sense to migrate it to math.stackexchange.com (thereby creating a duplicate question on that site)?
Here is one way it makes sense: Migration makes it possible to close the question as a duplicate.
Of course, I don't really see why that would be necessary when "off-topic" or "unclear" are often good alternatives.
Edit: Okay, the reason I constructed was a little far-fetched. Here's another way such an event might reasonably take place. Someone might click on the wrong option when choosing a reason for closing.
Here's a third way it might make sense. Some of the people voting to close a question might not read every sentence thoroughly, especially if a given sentence doesn't look very mathematical or looks like pointless noise. Instead, they may decide only on the basis of the mathematical content of the question that while not appropriate for MathOverflow, it may find a good home at math.stackexchange.com.
This is one comment on the question
I gave a partial answer on MSE, and I think the question should remain there. Voting to close here. – Todd Trimble
Now I do not know if Todd Trimble specifically voted to migrate or something else, but in any case it seems clear that at least some (and I see not reason to assume why not all) were aware of the situation.
IIRC, it was mentioned some time ago by a moderator here that they agreeed with a/the moderator(s) there (I believe it was Scott Morrison who said it and the m.SE mod that got mentioned was Willie Wong, but I might misremeber) that for "bad" cross-posts a reasonable procedure could be to migrate and then close as duplicate.
This question does not fall directly in the "bad" cross-post vategory as you provided a link youself, still I think by extrapolation it makes sense to proceed like this or at least to assume it makes sense to proceed like this.
Also, if the question is not on-topic here but is on math.SE then it should be migrated (or at least can be), whether it is a duplicate there is a priori not relevant. If one would start to take this consideration into account things would get complicated (what if I knew something will be a duplicate on m.SE, but not in such an obvious form?).
Finally, there are practical considerations: like
a migration-stub gets always auto-deleted for closed questions auto-deletion only happens under certain circumstances;
it makes a difference for latter (semi-)automatic maintance if something is actually closed as a duplicated or just closed differently and the text explains it.
closure as off-topic casts a downvote, migration does not (AFAIK, except it gets rejected on target site, but dup closure is not rejection). So, migration saved you from a down-vote.
I have a suggestion, which could serve to alleviate the concerns described here.
When there has been a vote to migrate, the OP is informed of the decision, and is asked to give consent. If consent is not given, the question automatically goes "on hold" as "off topic".
Once the OP has given consent, the question is moved to the review queue of the site being migrated to. If users there agree for the question to be migrated, it is migrated. Otherwise, it remains in MO as "off topic".
Given the concerns raised above, what do others make of this feature request?
I have expressed my opinion before and I reiterate here. Migrating to math SE (or anywhere else) is not ethically correct. We can only decide that the question is bad for MO, not that it is "more appropriate" for another site. As for math SE, from what I heard, it is populated by undergraduate students trying to cheat by posting their homework questions, and by mathematicians helping the cheating. Perhaps I am wrong, but if I am correct, migrating a question there would be even more wrong.
Edit For those who still do not understand why it is wrong: suppose that you submit a paper to Annals of Mathematics, and the editorial board there send it to Mathematische Annalen - without your approval and without even notifying you.