You're not missing anything. Systems like this assume there is a pre-created set of honest and independent nodes, which might later get hacked. They don't apply in the more realistic setting the PoW blockchain algorithm solves, where nodes can enter and leave the consensus at will and may be malicious or non-independent from the start.
You just do rounds of fixed sets of parties, like Ethereum proof of stake does. The set of nodes in each round are then needed to be 2/3rds honest. They then have Sybil resistance in each round as identities aren't free, since you need a stake in order to be selected for a round.
