If there were no potential slayers left then the Slayer line couldn't be passed onto anyone else from Faith. The girls don't need to be related to each other, they just need to have the potential to be a Slayer (although it was never really defined what determines this quality.)
The First wanted the bringers to kill all the slayers in training, their watchers and therefore erase their methods too. The First was then planning to kill Faith and then Buffy and then the Slayer line would just fizzle out because there would be no one left alive to pass the essence of the Slayer along to. They explained it in Dirty Girls.
*Spoiler*: However, in Chosen we see a multitude of girls of all ages becoming Slayers, so clearly the First wasn't even close to actually achieving its goal. I love the show so much but there were so many continuity problems in season 7 though that I think it's best to suspend disbelief for a lot of episodes in this season.