I think this depends on the goals of the system. For a game about a party of player characters that mostly collaborate toward an external goal (but go through some character development along the way) I think Blades does it pretty well. The use of Fate compels people describe above makes sense to me, too. In both instances. addiction is a source of complications that impact (without distracting from) the thing the game is mostly about. Vices matter in Blades because stress is an important part of your ability to complete scores, and overindulging might mess up your standing with contacts (who you need to complete scores).
Here it sounds like you are considering designs where addiction would be a more significant focus of play. I would say this only makes sense to do if your game is primarily about character development and relationships, because giving a topic like this nuance requires committing a lot of air time to it.
Also, addiction and recovery have a strong component of inner struggle and I think relatively few games handle inner conflict well. [Here’s a thread on the topic.]
Using systems that have the tools to make inner conflict an interesting component of play, here are two ways I think you could do it:
Dogs in the Vineyard Initiation, where the challenge the would-be Dog is facing is addiction. The player scripts the conflict as the version of themselves who is able to get clean. The GM plays out all the internal and external challenges to doing so.
Each time the GM pushes forward a die, they say something like:
- You find a bottle of whiskey when cleaning up an old camp site. No one else is around and they don’t expect you back for a couple of hours.
- Things are going well, which only heightens your anxiety. You know deep down it’s only a matter of time until you blow it.
- You’re into a another initiate who grew up apostates, he admits that he has a bottle of bitter church wine stowed in his pack. He wants to give it up and come clean, but he’s worried he’ll lose his shot at becoming a Dog.
The Burning Wheel, where a player character has a belief about addiction. “I have become a drunk, and I failed my queen; it cannot happen again.”
The GM introduces NPCs and situations that challenge that belief and test its limits:
- Introduce a rival who drinks too much, but has avoided the consequences (from luck or the strength of their name).
- Introduce situations with intense social pressure to drink, a diplomatic dinner or long sea journey.
- If the player character drinks, their actions push a relationship with someone they rely on to a breaking point.
- If they sober up, they still face judgement from others. Some friendly NPCs go cold, others act condescending or start to pry.
- Fallout from past mistakes causes economic hardship.
- Introduce an NPC that they need help from now, but have wronged in the past.
- They make a small mistake, unrelated to their addiction, and others assume the worst.
- Give them a reason to need privacy or trust (an important piece of intrigue, for example) and then have the people around them read their secrecy as evidence of a relapse.
I think it would take a lot of buy-in and agreement about expectations to have either of these play out smoothly, perhaps especially the Burning Wheel example, because of the prolonged focus on a difficult topic.
Another reason I included extended examples was to make a point (and clarify it for myself). If you are dealing with topic like addiction in detail, it makes sense to me to not make it a numeric system about manipulating your odds of success (+1/-1 to a stat, etc). Instead, it can frame the stakes of your character’s decisions and the consequences of your actions.