I saved this part for last because it's a very powerful argument, and I can't recall whether I've ever given enough thought to it or addressed it adequately. It's commendable that you raised the issue because it's pretty rare that I find someone postulating a daunting objection to my theology. Generally my theology is flexible enough to easily dispense with most objections. This one seems to be an exception.
On the other hand, it's a 2-edged sword, right? It cuts both ways. All of us, as exegetes, including you, must be logically inconsistent. You cannot legitimately embrace conflicting definitions of fairness and justice, even as you cannot embrace two disparate definitions of love:
(1) Kindness
(2) Cruelty.
That wouldn't make sense, right? If God can define virtues such as love, justice, fairness, honesty differently than we do, it undermines our eternal hope. That doesn't work, theologically.
So I ask again. If someone found a way to escalate your passions, would that count for YOU as a sinful nature? Is that justice, fairness (etc) as YOU define it? I think not - so you have to be consistent. Again, sinfulness isn't something that HAPPENS to me - it must be freely chosen on my part. Therefore God cannot really count it against a child - cannot count it as a reprehensible sinful nature - if his father induces in him a drug-addiction.
Why does God allow it, then? Actually I'm not 100% sure that He DOES allow it (I don't know if there's solid research backing this claim). But let's assume He does. What to make of it?
First of all, the child is already guilty in Adam. As such, he is born without "garments" (a shielding by the Third Person from excessive temptation). He is under judgment, and it is thus God's decision how much temptation is fair. Realize that ALL of us are born sin-addicted (and thus drug-addicted to some degree), due to Original Sin, but God decides the maximum degree of temptation facing each of us. Hence Jesus advised, "Pray that you might not fall into temptation." In sum, if God deems it fair that the child be born with strong drug-tempting desires, we have to assume such consonant with His righteous scales of fairness, and that He is a better judge of what levels of temptation are fair, than we are.
As a second possible solution, we could speculate that God only allows this infection-by-parent in cases where He has donated some of the parent's soul to the child (if He ever does that). In this case, the parent isn't really addicting someone other than his own soul, which is certainly fair. As I told you, my system is flexible enough to handle all kinds of objections.