I'd say a better angle to approach this from (as a DM) is, "Do I want cure disease to fix addiction?" If so, sure, it's a disease. If not.... then it isn't. . . . A lot of this boils down to, "Just how powerful do I want cure disease to be?" I would argue that it's a low-level effect and should be treated as such.
This is the approach I would take, too. Magic gets thorny when one tries to rationalize or mechanize it too much. I prefer to think about what I want the results to look like and then adjust the rules of magic (or the gods) accordingly. I like a world with addiction, mental illness, congenital disorders, heart disease, and lots of clerics and paladins roaming about. Therefore, cure disease doesn't normally affect such things. Even so, it is a world-changing ability (heck, that would be true even if it only cured
influenza).
In most of my fantasy campaigns, illness (whether mental or physical) is the result of either spirits or divine influences. Physical illnesses, therefore, might be the result of bad spirits (who congregate in swamps, cesspools, on rusty nails, etc.) or gods of death and decay. Cure disease is one spell that can help balance things, but many afflictions might be too powerful for it or other standard spells. Plenty of mumbo-jumbo and handwaving, but it usually turns out to be pretty evocative and fun in play. No cleric would be so bold as to say that one of their spells will
always work against some condition. The answer is always, something like, "let's see if I can overcome the evil spirits." If it doesn't work, a further quest might be in order, or you may be attempting to tamper with the will of the gods. This would be my answer to most congenital disorders... a person was born that way because of divine will, and that can't be undone by minor miracles.