Even with the modern disease model, there's so much societal shame around addiction that romance authors probably approach it cautiously as a potential conflict. As Leigh Davis pointed out in her article on addicted heroines, we're more likely to see it in heroes than heroines, and we're more likely to see it as a situational response to some other trauma.
Looking at romance heroes with addictions, it seems that we also tend not to see them in active recovery. Perhaps because of the way masculinity is associated with strength, self-sufficiency, and control, romance heroes are more likely to successfully tough it out and go it alone; often they've basically recovered before the story really begins. Typical examples of more macho recovery are Joe in Shannon Stacey's Exclusively Yours, who quit drinking cold turkey after breaking his brother's nose in a rage, Zane in Cut and Run by Madeleine Urban and Abigail Roux, who flushes his pills and stays clean, “because that was what Ty had wanted,” or Declan in Kresley Cole's Dreams of a Dark Warrior, who declares that he'll never shoot up again because, “I don't need to suppress my strength or get mindless again — I need to be strong and clear to protect what's mine.”
It's not usually that simple; just taking the first step of seeking help can be very hard, even for a supernatural warrior. In Lover Enshrined by J.R. Ward, vampire Phury goes to his first NA meeting and, “all he could think about was getting gone again.”