The reason why the families had a "no drugs" rule, was because they didn't wanna have a wide open rep they were drug dealers. After all, it's a dirty business. Especially back in that 1950s-1960s conservative era. Also, because of the long jail terms they didn't wanna have the bulk of their membership dealing, fucking up, getting pinched, and maybe turning rat to save themselves.

So, they allowed small contingents of their membership to "deal" with the approval of the bosses.

From the 1940s forward, Europe was a main supplier to the Americas'. Mexico was active in the 1930s, and later in the later 1950s-early 60s' also. But they provided "brown" heroin. Europe produced the "white" powder, and was their main supplier from the Middle East sources. Heroin manufactured by the French/Corsican, and Sicilians, was the main product.

Cocaine was NOT a big product for them until the early 1970s. Some guys handled it, but it was not popular yet, like it became in the 1970s-forward.

As you say, Cuba was also a main route into the southern states such as Miami and Tampa. For further transportation up to northeast and the rest of the country. But there were many ways to enter the states, and Canada was always a prime transport point.

And the Cotroni mob dominated these routes for years. They weren't the only ones, but the were the primary crew who moved the junk from there.