Not just The Godfather movies.
The rise of Castro and the fall of the Havana Mob | The Mob Museum
When the Mob Owned Cuba | Travel | Smithsonian Magazine
Mobsters in Havana: a brief history of the Cuban Mafia - Why Not Cuba
(You'll note that these are not left-wing sources.)
Pre-Castro Cuba | American Experience | Official Site | PBS
(The PBS site takes a slightly more moderate approach, but it supports the same basic idea.)
U.S. companies such as United Fruit and Coca-Cola had huge investments in Cuba. I've heard that United Fruit even helped partly finance the Bay of Pigs invasion.
US involvement in Cuba (both the US government and private corporations) was similar pretty much throughout Latin America.
Cuba was in a somewhat unique position, being that it was so close to the U.S., as well as being one of the last remaining bastions of Spanish rule in the Americas. After the Spanish-American War in 1898, we could have kept Cuba, just as we did with Puerto Rico, Guam, and the Philippines.
But instead, we agreed to withdrawal, provided that the Cubans agree to the terms outlined in the Platt Amendment:
Platt Amendment - Wikipedia
As for capitalist countries having more crime, this is also true. When I visited the USSR back when it still existed, I was amazed at how clean and safe the streets were. Even in a city of 7 million people. It didn't stay that way after the Soviet government fell, as there were huge crime waves which gripped Russia during the Yeltsin era.
Regarding capitalist countries, it's a bit complicated. I think the existence of organized crime has served the overall interests of capitalism, otherwise it would not have been tolerated as it has been.
I don't think it's as simple as having greater liberty, although I've noticed that when it comes to the legal world and lawyers, the measure of a person's liberty correlates to their net worth. Those who can afford the best lawyers get liberty, and those who can't get shafted.
Granted, I wouldn't blame capitalists directly for
that, as that's more a matter of our government and politicians who appoint the judges who oversee our legal system.