Using classic Outlook for Windows in business environments
Both Thunderbird and Outlook seem to exhibit the same behaviour.
I can get all inboxes to download using export.imap.mail.yahoo.com but something then triggers a 2000 message limit (as shown on Outlooks message count) in each folder.
Generally, the first "Send/Receive" after opening Outlook does it.
Then another Send/Receive triggers a massive redownloading of the messages in excess of 2000.
For me, it seems to be just Yahoo (rather than AOL which shares the same platform as far as I know).
It's clearly something funny about the way the Yahoo mailbox responds to an IMAP mail client starting synchronising.
On the positive side, I've been able to make PST file backups in Outlook during the times that all the messages were downloaded.
I think Yahoo may not be fully committed to their email platform.
I have to say Microsoft's outlook.com platform (as against the Outlook mail client) works much more reliably in my experience and that is where I'm planning to migrate to.