In this analysis nodes aren’t bothering to make sure that they have any connections at all. Shockingly, if a single node has no connections whatsoever then no amount of other connections in the system will make it routable. If instead every node enforce that it has at least three connections then these problems evaporate and everything works fine. I’m not being flippant here, this analysis really is that dumb.
Also there’s nothing wrong with long routes. They settle out in the middle just fine, despite the author’s dismissiveness to the possibility that they can.
This is not to say that a completely random homogenous network is an ideal or even necessarily a good way of setting up routing, but it works fine as long as every node makes sure that it has a minimal level of connectivity.