So far I've only skimmed the white paper, but I didn't see any response to this problem. (If the answer is "good guys can make lots of fake nodes too" then you're creating a computational arms race that will inevitably lead to just as much wasted effort as proof-of-work.)
There's also the minor practical issue that every node has to do an amount of computation and network traffic that's linear in the total number of other nodes, meaning the total workload grows quadratically with the size of the network.