Not only was this obviously false, but in Episode 7 we’ve essentially learned that Luke has also failed miserably in his attempt to bring peace to the galaxy.
Rey is a Kenobi
Ben Ostrower

Balance and peace are not necessarily the same thing. Anakin did bring balance to force by dismantling an over-powered Jedi Order that held influence over the government and acted as their army. Seeing the contradictions between Jedi code and Jedi deed sent him to the dark side.

Luke is the one that eventually helps Darth bring the final balance to the force, dismantle the Sith influence, and come back to a light(er) side.

Both the Jedi Order and the Sith are left in ruins after ROTJ.