I watched the same documentary. Yes, I was surprised to find out that they "elected" their commander (but that was a prevalent mechanism in those days . . . even militia in the US Civil War did the same thing), and I was also surprised to see in that documentary that some women were prominent "pirates".
Nevertheless, that documentary didn't inspire any "sympathy" for their lifestyle . . . for me anyway.
Yes, it was "democratic" up to a point . . . as long as they were making money (plundering and raiding). But the minute they stopped making money, there was a mutiny and they either threw the incumbent out, or most often murdered him/her and the replacement lasted only as long as they were making money. Then the cycle repeated itself. Hardly a democracy. The only democratic thing about it was that they voted on which site to plunder.