When you see a corrected design, you will understand why not being able to Sybil attack a frame of reference is what enables establishing blame and making the system Byzantine tolerant.
It won't work - you cannot combine the majority-is-truth rule with something which gives power to the minority, because if you do, any faulty minority will be able to overthrow the majority, which leads to divergent chaos.
It may work, up to its specified limits, but then it will fail a different way.
I find it amusing how monsterer often declares that something is impossible and then I show him it is possible, yet then he is so sure of himself again.
Making mining unprofitable combined with some different responsibilities for organizing the block chain produces a very different system in terms of the issues we are discussing.
Note some centralization is always required. Bitcoin gives us centralization but without any frame of reference thus observers have no way to be objective in order to use decentralized power to prove blame to all observers.
LCR has to do with converging consensus. It doesn't have to do with blame for example of which transactions get censored. Those can be orthogonal if structured in a way that allows unambiguously proving blame (independent of the LCR). In Bitcoin, when you submit a transaction to the network, you can't blame a particular pool for refusing to include it. No one can verify the claim by submitting it to network and identifying a particular pool that is the culprit. If you don't know which pool to blame and the pools are Sybil attacked any way, then you don't even know where to move your mining shares to (besides the fact that payers are not mining in Bitcoin because mining is profitable).