I agree that any blockchain has to be resistant to Sybil attacks. And that may be an insurmountable obstacle for my idea but, so far, I haven't let that stop me from thinking about it.
There do seem to be some properties of PoW/PoS related to the level of iniquity in control of the blockchain and to their incentive structures, and I think it is worth casting a wide net in search of something better (even if it may not exist).
It seems like everything might be a variation of one of two possible categories: economic game theory (Proof of Stake), or proof of committal of scarce, fungible physical resources. Everything else I can think of just seems like it'd be some form of centralization/oligarchy. But who knows?
(Proof of Stake is sometimes accused of being oligarchical, too, but I think it's still kind of the lesser of all evils, probably.)
What if the goal isn't to profit from block rewards but to attack the network, though? What if you pass stuff around over and over between tons of addresses you own? (Any person can create an unlimited number of addresses, pretty much instantly.)
Even if by the end the total transaction fees result in a heavy loss being incurred, the attacker would only do it if they think they can gain more from the network attack than they'd lose in fees.
I think a secure blockchain system can never make any kind of assumption that 1 address = 1 person/entity or 1 transaction >= 2 people/entities. I think depending on addresses or transactions in any way is probably a non-starter.
One of the key anti-Sybil features of Proof of Work, Proof of Space, and Proof of Stake is that it solely relies on a single scarce, unfakeable, totally fungible resource. The network cares about only one fungible variable: the total amount of computational power, or hard drive space, or funds in the network. That way, it makes no difference if the attacker has 1 address or 1 million addresses.