Why do doctors prescribe birth control for acne if there is a possibility it will all come back when you go off of the pill in the future?

It clears the acne. With any type of acne treatment, acne is expected to improve... and someday the treatment will stop. At that point, the acne may or may not come back. We treat acne because it gives clearer skin for the years during treatment (and patients are happier with their facial appearance). When treatment is stopped or weaned off, patients are older and acne is usually less or gone.