democracy promises citizens a government that is of the people, by the people and for the people which means that the people are the key element of what a society that practices a democratic government should be all about.
bitcoin serves same purpose as a currency that is of the people, that is created by a man or group of people that are concerned about the welfare of the people and that is at the same time created to serve the needs of the people and cover for the lapses of the government. a society, individual or government that believes and preaches democracy should natural want to adapt bitcoin since it aligns with her vision.
Technically it's a currency for the people (and one can argue how much it's a currency or money), but you are confusing this with DAO, and democracy doesn't even work with DAO, with that it's the richest who control the decisions.
This has nothing to do with direct or representative democracy. Bitcoin has nothing to do with welfare either, it's a protocol. It's a neat idea, but how do you even start to compare that with a government? Who do you call if you want something in your country fixed? A bitcoin developer or to your representative in the parlament?