A General History of the Pyrates is not the only primary sources on the so-called Golden Age of Piracy and the attempts to reign in piracy. There are tens of thousands of archival and print documents related to piracy in the Caribbean in English, Dutch, French, Spanish, Portuguese, and likely many other languages. Among others, these sources include early newspaper accounts, court cases, prize court proceedings/interviews, letters from government officials, defense documents, private shipping records, family and estate papers, travel diaries, travel narratives, witness letters, and interrogations of victims. Many of the printed texts on piracy are available digitally through archive.org, the John Carter Brown Library, Early English Books Online, or other academic libraries.

Held against the sheer volume of primary sources available, this text is not a particularly reliable one. As you mention, the text was published under a pen name. Although scholars have proposed Defoe and Mist as likely candidates to have been its author, we don't know for sure, for sure. The book combed the sources that I listed above to construct its narratives, but also mixed facts with rumors, personal anecdotes, sensationalism, exaggeration, and outright fiction of unknown providence.

Why did the book become popular? Perhaps this would be better left for literary scholars, but I would say that it was its mix of fiction and nonfiction, truth and exaggeration that made it popular. It was an engaging text, published in English, that appealed to an audience thirsty for just such a popular piece about something that they would have heard about. It was heavily advertised in newspapers. It was widely available in the Atlantic world. It humanized, while it simultaneously included scandalous and unusual biographies (e.g. women pirates omg!!). It included lots of asides and personal first-person commentary that appeared to be first-hand knowledge from an expert. It included lofty, ambitious commentary on society and individuals, which appealed to the reading public. I also think that it is key that the book went through multiple editions, which highlights the process of early modern editing/embellishing. Later editions corrected previous errors while adding additional materials and sources. Multiple volumes and editions demonstrate how popular the was, but it also made the text even more widely digestible to the reading public. Finally, I see a bit of a confirmation bias at play here. The book was "nonfiction," but fiction about pirates published at the same time paralleled and confirmed its interpretation. The book therefore helped to establish many tropes of piracy, all while it was shaped by the tropes that had already formed within early modern popular culture.

That is the challenge of working a topic like piracy for historians. The easiest sources to access are often the least reliable, yet they hold a preeminent, often undeserved/problematic place in popular memory precisely because they created the tropes by virtue of being popular and easy to access. To dig deeper means going into the archive to access other sources or ask new questions of known sources. Or it means using archival sources or more reliable but lesser-known texts to verify details in popular print sources. After all, most sailors of the early modern period were not literate. Only a handful entered the historical record. Plus, pirates were criminals: smugglers, thieves, robbers, murderers, rapists, and human traffickers. They did not want to get caught (and therefore they did not want to enter the historical record). Historians have to do extra legwork to access the few direct voices that have survived. They have to be clever about their use of sources to mine seemly unrelated sources. And they have to resist the tropes themselves, which can trap their thinking.