I thought about similar for a long while, pre-Bitcoin even. I think it's impossible to do money as such. Bits don't have an intrinsic worth, and so value is always in relation to another party. A key property of money is fungibility, thus network effects from many people using the same definition of value. Thus, central authorities, whether those authorities are controlled by fickle individuals, natural language bureaucracies (traditional companies), or formal language programmatic consensus (blockchain).

I think about the only decentralized improvement one can do is software that creates credit lines denominated in an existing currency, between mutually trusting parties. And then attempt to scale that up (ala Hawala), with technical means to keep the slightly diminishing fungibility from being an issue (one USD owed to you by the Treasury is worth slightly more than one USD owed to you by your friend A (owed to him by B, and so-on), even if you trust A with your life).

However, there are many areas where we can adopt decentralized functionality (which actually means not having unnecessary centralized functionality), such as my above naming example. If we want decentralization, it's just ridiculous for my browser to be making hundreds of centralized name lookups to render a single page. And I've seen too many blockchain projects where they're actually pushing a solution that is more centralized than the existing ones.