At present, payments are too centralized, and too prone to being spied on or choked off by authoritarian governments. Another consequence of centralization is that cross-border payments are unnecessarily expensive.
A number of proposed solutions involve distributed public databases, rather than a fully decentralized network. This isn't ideal from a privacy perspective, and is still subject to effectively centralized decision-making about changes to the nature of the database.
The long-established hawala system comes closest to solving this problem; an automated hawala-like network running over the internet could realize decentralization's efficiency and privacy benefits, bringing them from hawala's home around the Arabian Sea to people in the rest of the world, both those surviving under authoritarian governments, and those living in freer countries.
Eventually, the solution should scale up to payments of all sizes, in and between all currencies, and maybe even include other sorts of financial instruments.