Additionally, XEP-0444 (Message Reactions), and pretty much anywhere an ID will ever be used to reference another message.

The issue stems from XEP-0308 replacing/overwriting the message ID, and consequently all references already using the previous message ID are left pointing to a non-existent message.

Amongst other things, this provides a way to avoid moderation — send an offensive message, it gets moderated, just LMC the message and it's no longer moderated.

So, while it feels 'wrong' from a purist view, NOT replacing the message ID would be the better option - old and new references will then all point to the same message. Otherwise, presumably, clients (and servers?) will be required to track all past message IDs for each corrected message.