I would do everything legally. Let a judge decide.
My son's AD was out of his life for 10 years and has only just now come back. I sought sole custody -never asked for child support because i, like you, didnt care about the money. I actually felt that the money would mean he would be stuck in our lives forever and i wanted him away from us - i never denied him visitation but had all the rights so i could be the one to decide when and where it was appropriate. He had no legal obligation and pretty much just went away on his own - which was a relief to me.
So did it affect my son not having his dad? Yes - he has abandonment issues
Do i think it would have affected him more having his dad? Yes.
Does he blame me? No - surprisingly since he blames me for everything else but he doesnt blame me for his dad and i have told him the truth about everything i did. Even if he did blame me I would still do it the same way because its what was best for him.
I never dogged his dad to him but i did tell him when he got older that his dad was an alcoholic and just wasnt capable of being a dad. Not everyone is. I made a decision when my son started asking that I wouldnt let him see his dad until he was old enough to protect himself and get out of dangerous situations. Last year his dad came back into his life and he has caused so much confusion in my son - its starting to seem like the pain of having dad in his life has been worse then the pain of being abandoned. my son goes back and forth - when he wants to get away with stuff he prefers being around his dad who doesnt care what he does. So even though I agree that genetics plays a higher part i also agree with you because his dad did allow things that were unacceptable. When he is in a stable place he knows that his dad cant be a dad and he stays away from him.
You have to do whatever is best for your child today - you cant worry about the future. Love your child in the best way you can and seek him safe - what happens in the future you cannot control.
As a side note - through experience I know that addiction is more than just what you learn from your parents. My son didnt spend much time at all with his dad during his life and I gave him a very stable home but he is still exactly like his dad. He talks like him, behaves like him and is an addict himself. There are so many little similarities that i thought were learned emotions but arent. So there is a lot of genetics involved in this. I say that for those out there who are considering having a child with an addict - the genetics are going to give them a predisposition to addiction.
Kind of off topic but I've seen some bizarre similarities and this one is the most visual. I gave my son the Moon when he was a little boy - just a game we played one night when the moon was full. He then picked out a star and gave it to me. Later on he made a moon and star symbol that he said represents us and its been our symbol for many years. It was really sweet but what freaked me out about it is that his dad has had the exact same symbol tatooed on his ankle for about 25 years - long before i met him. About two years ago, before he met his dad, he said he wanted to get it tatooed on his ankle when he got old enough. Again i was freaked out - not only the same symbol but in the same location, but i never told my son about any of it. When he met his dad and saw it wow was he freaked out. What's the odds of that one?