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).
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
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).