UUCP is a hierarchical network (people configure a few paths to neighbors and they take care of the rest of the delivery), and BGP also requires pretty specific configuration and setup. Here we're talking about a single broadcast domain that automagically configures its paths and takes routing decisions.
There are such protocols (like BATMAN) that can create such mesh networks, but they still fall short of that many nodes. Not to mention the whole hell of assigning IP addresses (it would work with v6 and SLAAC, but ipv4/rendezvous and the similar things will be a problem), level of trust for neighbors, etc., etc. In the end what we would need is BGP's policy routing with zero need for configuration and convergence times that are less than a minute, which might be just too hard to do.
(and there's a reason I say this has to be automatic, just think of a bunch of average users doing policy routing and the resulting mess)