Addiction usually starts from escapism, and the causality that drugs cause addiction is very far from true.
I'm not arguing your second point, but suggest you consider that some drugs are more difficult to quit and are therefore more addictive than others. I'm arguing that people who have problems with drug addiction will likely add more legal drugs to their stack rather than curb use.
Do you also want to ban everything except heterosexual copulation for the sole purpose of procreation because there are sex addicts?
Shall we do away with video games, playing cards, dice and horses because some people have problems controlling their gaming and gambling behaviours?
How about making it illegal to own pets because some people neglect theirs? The same goes for having children.
Are we banning all food except reconstituted, fortified, protein—fat—carbohydrate sludge because some people have eating disorders?
I think you're letting emotion blind you since it seems you're not actually reading and understanding what I write.
Of course, your mentioning of polydrug use could be just a neutral observation, but why then use it as an argument?