Every user of Bitcoin, who is online, is connected to every other user.

I can send a message (txn) and he can get it. Push.

This is very powerful. Instead of an IP though, you have a BTC address.

A P2P network that allows you to push messages to other users (bouncing through various nodes) in in effect - the same as the internet itself.

The current design of the internet does not distinguish between different routes across the web.

Is there not a more sustainable design - where the most used, the routes that transfer the most data, pay more for their usage? Those routes would require the largest routers to handle the traffic, BUT would make the most money if users had to pay fractional amounts to transfer data.

Say you try to access BTC://NETFLIX over the current Bitcoin P2P network. Not as a flood fill obviously (which is what BTC normally does) but just for routing purposes. The messages would only be bounced through the required nodes to get to you, no matter how far behind a NAT or firewall you may be. (We're all connected after all)

You or NETFLIX depending on the business model would need to pay for the use of that bandwith. The incentive structure would be there to offer those data routing services.

The LN network - is a P2P network of already P2P connected Bitcoin Nodes.

There is an overlap there, that you could make generic, and let people connect to other nodes for any reason they like, as long as they pay for the bandwidth used on the data hops.

Sorry - I'm rambling. There just seems to be a powerful property of a large scale P2P network like Bitcoins that is being under utilised.