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.
Democracy talks about the freedom and the will for the people to easily choose what they feel is right for them, and bitcoin encourages right for societal growth and creation of individuals wealth. Left alone with the government, just like you said, there lapses are just too many, from unfulfilled government promises, to a system that is rigged for the favor of just a few and a whole lot more, so the right for self custody of your wealth as against the manipulative system of government is what Bitcoin encourages, so a true Democrats should love Bitcoin.