Sorry but I have to mention that Nazi Germany became incredibly prosperous, but it decided to use its wealth to obtain military power.
Also, Europe dominated the world for a couple of hundred years before the Great War. Some parts of Europe may have been poor during that time, but compared to the rest of the world I do think it was a whole lot better.
Japan was incredibly rich in the beginning of the 20th century - and it was definitely not a democracy. Australia, Canada and NZ are all part of the ex-British Empire and I would say that's what made them prosperous, not their political system.
South Korea rode on the back of US support, like Japan after the war, but I do agree they did that while being mostly democratic.
Uruguay has just very recently become a nice place due to basically a single guy! That president, Jose Mujica, was such a legend! And a big critic of capitalism , by the way.
Taiwan was what we used to call the "Asian Tigers" that became rich in an incredibly fast manner... I don't know that you can attribute that to a political system at all: Singapore was and is a dictatorship and is perhaps the best example of Asian Tiger - it became richer than Australia in like 20 years!
All in all: you do not convince me. You do not seem to understand what made those countries rich in my opinion and you haven't really reflected on it if you really think that democracy was the common theme.
EDIT: Taiwan is a tiny island, China is a huge country. The GDP percapita of Shanghai and Beijing is about the same as Taiwan... Hong Kong and Macau, also part of China, have much larger GDP/pc still.