Flow is limited by the narrowest pipe along the path, and my suspicion is that you would need to get to pretty damn high user adoption before you could expect consistent, high flow between points since you'll need to find many alternative paths. Prior to that level, the network wouldn't be very useful.

Still not entirely sure what problem this solves. As a consumer, I don't really have an issue with current payment systems. I can buy everything I need in seconds, and banks compete for my business by (as stated elsewhere in this thread) giving me kickbacks from the fees they take from merchants.

As a merchant, you're not going to trust your customers/suppliers at the level that would justify extending an unsecured line of credit to all of them. Not going to happen. Yes, perhaps payment systems suck, but honestly payments are an incredibly hard problem. A robust legal system which enforces contracts solves the hardest problems, I suppose, but legal action is slow and expensive so it's still pretty hard.