The streams work in a hierarchy, with the uppermost assuming the highest network burden. Because it's necessary to send an acknowledgement message, a complete circuit must established (though not all at once) between nodes.
Also "broadcast messages" seem too risky to me. They're liable to be abused and cause a DoS if this protocol is adopted on a large-scale.
Proof-of-work doesn't protect broadcast message abuse, because an attacker could just use a small botnet to generate a bunch of untransmitted messages with similar timestamps for a future date. Once that date arrives, then the attacker could just submit a very large batch of valid broadcast bitmessages.
I can't think of a solution to either of these problems right now, but I otherwise think Bitmessage is a great idea. It's current, humbly sized userbase makes for comfortable testing.
James