Well, they aren't really pirates if you need to take that amount of effort, and if they can be eradicated easily. If you want to take care of them on the sea, your trade is grounded until you get drydocks. On the other side of the spectrum, you can just take them out first thing if you are a faction with a colony in the Americas.

Neither of these options are really fitting answers to historical piracy, so CA really does need to change it around.