This sentence blows my mind, and I don't know enough to understand it. Could someone helpful point me to a relevant Wiki article or something to help me grok how this could be possible?
I don't think it's fair to say that as a generality. The stability and latency of the network very much depends on the routing protocol used as well as the strength of the connection between the nodes (assuming it's a wireless mesh). There are many routing protocols that are more robust. Some protocols are tolerant of devices moving, some are not. Some are self-healing, some are not. Some have to map out the full route to a device before sending data, some are only aware of the next hop.
There are a lot of options, each with their advantages in different situations. It's not so clear cut. It can be fast or it can be slow. It can be stable or not. It very much depends on the particular network protocol and setup.
Reading your comment I felt we agree on the facts. For personal opinions, I will reiterate: I don't see it happening in practice. Cool idea on so many levels, just the incentives aren't there to make it happen in current society.
Since I can't reply to your last two comments (too deeply nested I guess), I'll comment here.
I agree that right now it's not going to happen, no matter how many different efforts there are out there. For it to really happen I think we would have to come up with a plan that would actually work, in terms of creating a massive world-wide mesh network. There would have to be a lot of consideration for things like security, DDoS mitigation, speed, standards and upgradeability.
If developing a viable mesh network for the task weren't tough enough, there would also have to be a plan for migration which is really the hard part. Getting everybody in the world moved over to a new network would be nothing short of a miracle.