If you take drugs and get addicted, that's your responsibility. Not anyone else's.
Think so? I can introduce you to some former surgery patients and war veterans among others who were introduced to opiates to control pain by their physicians for very real pain problems and as a result were unable to avoid addiction. I can point you to some suffering from PTSD (not their fault) who are trying to find some way to cope who sometimes turn to chemicals because they don't understand what has happened and it is the only relief they can find before they understand what has happened. Some addictions are not the solely the fault of the person taking the drugs.
It's easy and wrong to paint every drug addict with the same broad brush. Some, like the sort you are thinking of, are simply idiots seeking pleasure or escape. If you are snorting cocaine on your yacht for fun, yeah that's on you and if you die I'm not going to cry a river for you. Others are decent people trying to cope with a real problem not of their own making. You really think that a wounded veteran who gets unintentionally addicted to opiates while trying to control pain is solely responsible for his situation? If so you are a very cold hearted person.
I think you're conflating "responsibility" with "fault". The addict has the responsibility to deal with the addiction and manage their life, regardless of whether they are morally culpable for becoming an addict. Just as they are responsible for their actions if, for example, their addiction drives them to crime in order to support their habit, or they cause harm while under the influence of the substance that they are addicted to.