To be fair, the theory that economic development leads to political liberalization isn't entirely fiction. Taiwan and South Korea both used to be de facto dictatorships.
Also, it may be worth dropping by much of the Middle East to get another reality check on this question.
The only thing economic development seems to consistently result in is a higher demand for imports.
[1] Well, the nice parts of it are much wealthier than they used to be. The provincial towns are dying, and all the productive industries have been pushed out by oil and services.