I think it would be more accurate to describe a democracy as proportional representation of opinions. Bitcoin is like a democracy with a minority government. The miners are simply casting votes that say "I should get all the Bitcoins!" And by a convoluted process, a ballot is drawn so that someone indeed gets all the Bitcoins roughly every 10 minutes.
How the reward is divided up has nothing to do with rules and forces no one to acknowledge someone's reward if they didn't follow the rules.
Also, are you forgetting that political systems are generally shaped by history? If a so-called democracy evolves out of a monarchy, it's likely to have many features of the previous system, such as a large bureaucracy and a police force. Or, more generally: structure. What would democracy be like if it started out with no structure? Or at least a certain bare minimum that is needed to enforce the system?
You are clueless about history and how the American republic looked like right after it's inception. It had 0, yes 0 "features" of a previous system, because there was no previous system. It's the last form of government, the last algorithm that was invented from almost a completely clean slate. People were actually nut just free, but sovereign and owned what they produced. Their privacy was sacred and they could do or own virtually anything that didn't hurt someone else. A far cry from today. What they have today is a gradually corrupted government into a fascist corporatism that evolved because while what little power that the original limited government had, there still was some power to be auctioned off, and guess what, special interest bought it all up and controls it today.
The only answer moving forward is not back to the same recipe for inevitable disaster but forward with something new and even more radical. No central government with no power to be auctioned off.
Btw I bet you don't even realize that you are a slave today and what it means to be a sovereign and truly free. I'm willing to bet money on it.
None are more hopelessly enslaved than those who falsely believe they are free.
- Johann Wolfgang von Goethe
And Bitcoin, if you didn't realize this, is a tool some slaves are trying to fight back against their masters.