We really need this. We're having the exact same problem everyone's mentioning. Clients reply to an old email without the case number and a new case gets added. We just had a case opened 3 times because people kept replying to an email without the case ID. I ended up doing the resolve as duplicate for the latter two cases, but each case had separate important information. I ended up just copying the message from the last case into the first one (the 'real' one) and closing it.
Since they're all opened as email messages, you'd just have to add the replies in timestamp order to the main case. You wouldn't have to worry about merging and resolving properties and all that, keep the main case exactly the way it is, and just add the messages from the 'duplicate' cases.
You say you have no use case for this, but everyone's saying the exact same thing, just add the messages from the latter cases to the original one. To get to your points:
1) Yes, just interlace them. No, it wouldn't destroy any coherence as most of the time the emails just add more info.
2) The merged case looks just like the original only with the messages from the others added in. It would have the properties of the original. It is different than closing as duplicate since the messages of the 'duplicates' are now in the original.
3) It is really inconsequential how the user is notified. The important thing is that all the messages are in one place. If you really think the users need to be notified, then ask yourself how the correspondents of the duplicate cases are notified when their cases are closed as such; and how the correspondent of the original case gets notified in such a case... Just do the same thing, except instead of emailing them with "your case XX has been closed as a duplicate of case YY", say "your case XX has been merged into case YY".
4) Yes, it absolutely would be worth figuring out how to do it, in fact I just did.
Either that, or just have your email system be smarter and not rely on the case ID being there to figure out which case an email is for. Usually the original text is quoted in the new emails.