But... it's how everybody talked back then! Come on, Ron... play along!

Pirates ARE a pop culture concept. Nobody really cares about the historical accuracy :D that's why kids love them and that's also what the Monkey Island humor (especially in 1) is based upon. I love this concept and  I think it's pretty unique, pirates are the only "group" that actually existed, but are now seen entirely differently  and almost like fictional. Knights? Hippies? Romans? Always way more facts-based.

To me ARGHHHH comes from a thirsty man at sea drinking just Grog:

"Sailors require significant quantities of fresh water on extended voyages. Since desalinating sea water was not practical, fresh water was taken on board in casks but quickly developed algae and became slimy. Stagnant water was sweetened with beer or wine to make it palatable, which involved more casks and was subject to spoilage. As longer voyages became more common, the task of stowage became more and more difficult and the sailors' substantial daily ration of water plus beer or wine began to add up."

So I am 100% positive that pirates said ARGGHHHH, because they were thirsty, and probably dragging Rs because they had to be drunk to be hydrated. So I believe the Hollywood talk for that reason.

https://en.wikipedia.org/wiki/Grog

"...their Speech would have been that of an underclass British sailor..."  coupled with "...most of them came from London..." practically confirms that pirates spoke Cockney. Can't wait for the first brave soul who tries to implement that in a game or film.