They don't want to stop overeating. Anorexia gives them an excuse to eat a shit ton of food under the guise of it being 'healthy behavior' (I.E. I don't wanna slip back into anorexia! If I count calories it will drive me back into mah disorder!) But if they latched onto binge eating disorder (which a lot of them probably have) then any time they try to use it as an excuse people could just retort by telling them they are being unhealthy. They cant use it as a shield in the same way.