POP has never worked when accessing mail from multiple computers. The best you could do is leave everything on the server. Point being, if you want to access your mail two different ways and have it be consistent between them, POP has never been a possibility. POP was only ever designed to transport mail from a server to a client. It's the final level of delivery.

If you don't like the way that Gmail runs its POP backend, don't use it.
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Bitt Faulk