Your list contains a large number of West European nations, which had the fortune of... being in West Europe. I.e., the fact that they are wealthy and free are more likely explained by past history, rather than one causing the other.

South Korea is an interesting case: it used to have a worse economy than NK, started rapid economic expansion while under a corrupt dictator, suffered through another, and could not really be called a "democratic" country until 90s. So maybe prosperity eventually causes democracy, but it's a slow process.