Well, I think what you proposed is better than Bitmessage. But to end user Bitmessage provides same benefits (+ a few backdraws). I have been thinking exactly what you have proposed. But based purely on DHT, with intermediate hops and message polling when retrieving data, without direct connections between clients. If you have read freenet's freemail implementation paper, that describes parts of the process. Because freenet is distributed encrypted key/value storage solution.

Basic feature of DHT is that data automatically expires after a while if not refreshed to group of nodes. This would allow more efficient routing that what Bitmessage does. That's one of the primary reasons why I don't like it. I also suspect that a key streams in bitmessage could become overloaded, because there's no way to loadbalance key streams.