I think that an argument could be made that while old age and diabetes are unavoidable health issues at this moment in human history, addiction IS avoidable, so if there was a natural disaster and you were able bodied but unable to help others because you were dopesick, it would be because of an avoidable and self-inflicted ailment. Obesity is basically an unhealthy addiction to food in my opinion so I would put the obese in the same category as the addicted. Not saying I necessarily agree that this means addiction is a bad thing, I just thought the natural disaster scenario was an interesting talking point.
I think another argument could be made that being an addict is like driving drunk... while some people might manage to do it while keeping their own lives and the lives of others intact, there is an increased risk of causing harm to those around you, and this is an area in which people frequently overestimate their own ability to control themselves, despite evidence to the contrary.
Even if everyone was capable of keeping their moral compass pointing in the right direction while deep within the most hellish addiction imaginable, it's still hard to find a reason that it's not a bad thing for a human being to be reliant on an externally administered substance in order to feel normal, for reasons that are not purely medical. Of course that doesn't mean there should be any stigma, because most if not all addicts probably start out trying to self-medicate some kind of mental health issue, so while the above examples are potentially explanations for why the stigma exists, I think for the vast majority of people the stigma is just a cultural habit, where drugs are somewhat demonized, plus the fact that the majority of visible addicts are problem users, and they probably just haven't thought about it much beyond that.
It's possible to imagine a more progressive, compassionate society where addicts are not looked own upon at all, but this society probably also takes steps to prevent the kind of circumstances that cause drug addictions in the first place, and provides a far more comprehensive range of options to help people out of their addictions, rather than just letting people get on with being addicts.