My understanding is that it was basically that, once prohibition of alcohol in the USA was ended, the agency which had been built up on the basis of prohibition had to find something to deal with, or it would have been in danger of getting wound up, and marijuana fitted the bill - with the big advantage, at the time, that it was disempowered people like Blacks and Mexicans who tended to use it.

And the rest of the world just followed Big Brother Jonathan, which is often the easiest thing to do.