Earlier quoted context omitted.
Determining fully decentralized consensus between arbitrary participants (or at least one of the best approximations of that). In Bitcoin that consensus is limited to transactions, in Ethereum with smart contracts it can be used for much more (though that might require additional layers of incentivation to work properly, depending on the use case).
Nobody actually wants fully decentralised irreversible consensus between arbitrary participants on a public ledger because it is slow, costly and doesn’t solve real-word problems of identity verification, trust, reversible transactions, private transactions etc etc. People have tried and failed for years to find a compelling use for it. It’s a very interesting experiment in social engineering but I find it difficult…
Are you sure? In fact it seems like quite a few people want that, as evidenced by the entire crypto space.