In the specific case of currency, practical double spends are a real issue. 'Merging' the state after a double spend requires either forcing the double spender to pony-up, or taking back money from those who received it without being aware of any wrongdoing. That is, unless you are fine with people printing their own currency.

This is rather unique to the case of currency though. Specifically, the history of transactions determines which future transactions are possible. Instead a system that only records promises (but doesn't allow transfer of such promises) would work without centralization. If I promise something to 2 different people I remain on the hook for that promise. The fact that I am effectively 'in debt' on the system isn't an issue because the system gives no guarantees on people meeting their promises.