How did the node get started in the first place though? Unless you were part of the genesis block yourself, you only believe the history at all because someone told you it was the right place to start.
In full PoS in the model I described you'd need social consensus to determine the allocations in the genesis block. In PoW you need social consensus on the genesis block as well - the PoW algorithm, the initial difficulty and block reward, the difficulty adjustment algorithm, the block reward schedule
I'm not saying that requiring clients to log in every 4 months is a reasonable security assumption, just showing that hand-waving it as "completely circular" is incorrect. It's more nuanced than that.