Constitutional monarchies tend to be good, stable, prosperous countries: coincidence?

I'd never really thought about it before, but it's true: most of the most prosperous, open, stable and progressive countries in the world are in fact constitutional monarchies. Think of Canada, Britain, Australia, New Zealand, Sweden, Denmark, Norway, the Netherlands, Luxembourg, Spain, Belgium, Japan: yup, they all have kings and queens (or emperor in the case of Japan, but same idea).

Coincidence? Maybe. Correlation is not causation, as they say. And monarchs typically have next to influence on the political system of the country, with the kings and queens (and emperors) playing almost no practical part of the actual running of these countries: their roles are almost entirely symbolic. But it still seems like quite a coincidence, no?

Actually, if you look at the Good Country Index, 5 of the top 10, and 11 of the top 20, countries are constitutional monarchies. So, only about half. But consider: there are only 43 constitutional monarchies worldwide out of 206 sovereign states, i.e. about 20%. So then the "half" mentioned above becomes a lot more significant.

Anyway, I won't belabour the point. But food for thought.