So from what I can tell,
The fairy dust is just "fairy-poo"
I don't see why Black-Beard couldn't just work out some sort of waste-removal deal with the fairies.
I mean, Black-Beard gets to live forever, and the Fairy kingdom get's free poo cleaning..
Like what's the problem..
Look what happened at the end of the movie, The fairy lock themselves up, and they gotta live in a giant cave with all their poo stuck on the wall..