Oh, horse puckey. You're cherry-picking a bunch of Latin American countries, all of which have a similar culture and history even excluding religion. All them are not "inherent failures of despotism," either. Costa Rica is certainly not. Chile is arguably not. Colombia is arguably not.
Now consider countries that are not Latin American, but still Catholic. Poland, despite being occupied by foreigners for much of its history, was reasonably prosperous until war and Marxism, imposed from outside, changed that. Malta is hardly an "inherent failure of despotism". Czechoslovakia, which was majority Catholic, had the highest standard of living in Europe before the war.
Uh, I would say the entire majority of Latin countries in Central and South America support my take, while you cherry pick the very few that could even hope to show something positive from their resources. I love how you use a country in which prostitution has always been legal (Costa Rica) as a great example of positive Catholic influence. You must love your pope!