If you need to send a bit of info to your physical neighbor, a mesh network might be a good solution. If you need to send a kilobyte to your friend half the world away, a mesh network would need to have a great number of hops.

If it just so happened that you are one of the few users with a mesh-network connection to a peer across the street, much or all of the traffic between your street and the next street will pass through you. Since it's a mesh network, you are expected to have a low-power, low-throughput node, which might be overwhelmed.

Do not conflate mesh networks (of nodes in physical proximity) with peer-to-peer networks (of nodes in logical proximity via all of the Internet).

I'm not - I think :-)

There is no particular reason a mesh network needs to be low power and low throughout - I think one of the most potent mesh network opportunities is (slowly?) replacing in home routers with (firmware?) to communicate amongst a neighbourhood. With that a small and growing group of people will be able to exchange local data and video and voice.

I perhaps naively think that physical proximity will become a major deciding point in bandwidth between two nodes (which makes sense) and this will encourage an explosion of useful local perhaps democratic applications - think of it as garden fence protocol. Sharing not just pirated films but kids calling their neighbours to just chat, parents arranging bar eques etc