I got also bitten by this. While IMAP would allow for syncing, most MUAs don't have a local mailbox. Instead they have a cache and the offline mode means to put as much as possible in to the cache. But if you want an actual local mail storage, you will eventually have merge conflicts, because how do you deal with a message that is present locally and was on the server, but is no longer? Do you assume the user wants it deleted, or that it should be reuploaded to the server? Either way will be wrong. (Also if you reupload, it will get a new UID, so another MUA will again reupload it, i.e. you will get a copy per MUA.)

So if you want a mailbox sync tool, use a proper program for that like mbsync/isync. (But this can't cope with cross mailbox moves besides (not) propagating them.)