Jerseycity, I'd say that interest in pirate culture was at a frenzy from the early 2K's to 2k10 or 2k11 thanks to Disney's 'Pirates of the Caribbean' films, but interest in pirates in general has been very strong as long as I can remember, and if you ask anyone to name a real-life pirate from history, 7 out of 10 (or more) are probably going to say Blackbeard (although I'm conviced some will first say Long John Silver or One-Eyed WIlly). That being said, of those people that say Blackbeard, most (if any) won't be able to tell you the name of his ship (or the names of any real-life pirate ships for that matter as most would probably name fictional ships like The Black Pearl or the Flying Dutchman or real-life non pirate ships like The Bounty), despite the likely discovery of the wreck of the QAR in 1996 or the years of relic recovery and museum exhibition of those artifacts.
In fact, most people who dont already have a vested interest in historical sailing vessels probably didnt even know the name of Blackbeards ship until they saw the 4th PotC film, and have probably since forgotten the name of the ship.
The problem that really arises is that no one actually has an accurate description of the appearance of the ship outside of the fact that it was originally a British Frigate built in 1710 known as the Concorde which can only give a vague idea of what she might've looked like. Then you have to take into account modifications done to the ship by the French and then finally by Teach's crew. I've read varying reports that Teach did nothing to the ship whatsoever (as reported in 'A General History of the Pyrates'), to reports that said he modified the ship to carry as many as 26 additional guns (added to the 14 guns she was rumored to already have), but there's really no way of actually knowing, which means that anyone could probably just build an early 18th century British frigate, modify some extra gunports and guns and slap Blackbeards colors on her and call it the QAR. Although I think it'd be great for a reputable company to put a kit out there, as long as it does the legendary ship justice and is as historically accurate as it can be made based on the sparse evidence that we have avilable on it.