The game heavily implies that the Fireflies are not exactly "nice people" or "noble". Would they have distributed the cure to everyone? I hardly think so. That is assuming the cure actually WORKS of course.
And, even if they did, how they would do that? There's no way of distributing the vaccine around the world. Not only that, but civilization is completely dead at this point. Even with no more infected, I hardly think people would go back to being "people", instead of just animals fighting for survival. Hell, many people would probably not even agree to take the vaccine.
Not only that, but the world took EVERYTHING from Joel. Ok, so let's assume best case scenario - the cure works, everybody takes it, the infection is gone, civilization starts rebuilding itself... and then there's Joel, with NOTHING left AT ALL. Great life huh?
tl;dr: the world is too fucked up to be fixed and Joel already suffered too much.
