I don’t think the reason that public drug use is prosecuted is because it offends people prima facie. It’s because it’s associated with and indicative of a more serious problem: addiction. Addiction fuels all kinds of crime. The same cannot be said of passing gas.
I agree with you that addiction can be a serious issue, but I have some responses to that.
1) If someone's addiction leads to crime, then punish the crime when they commit it. Don't make the pre-crine a crime. Instead of preventing crimes, now you've multiplied them.
2) If drugs weren't ruinously expensive due to their illegality, there would be much less need for addicts to turn to crime. You don't normally hear about alcohol, cigarette or coffee addicts going on crime sprees to support their habits.
3) There's evidence that responding with properly funded support and treatment is cheaper and leads to better outcomes than a massive carceral complex.
4) We can discourage a practice with lighter punitive measures than prison. Running a red light is a rampant traffic infraction, and potentially deadly to boot, yet we don't typically punish it with jail time. It would be massively unproductive to do so. We typically fine people and/or give them "points" on their license. Similarly if needed, we could discourage drugs with fines, taxes, restricting privileges, mandated treatment or social shaming instead of incarceration.
