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> A single message often needs to be in several different folders simultaneously.

Citation needed. This has never occurred to me.

> And when the thread is spread across many folders, there needs to be a way to see the whole thread.

Already possible, at least in Thunderbird.

> Labels are a fundamental feature [...] and neither IMAP nor POP can handle them gracefully.

IMAP has user-defined labels, whats wrong with them?

An underrated feature of IMAP is that you can attach notes to mails.