I'd bet the percentage of people that would rather pay to imprison people, rather than deal with the treatment / relapse loop is at least 25%. Likely even higher if you take it as a percentage of the gainfully employed.
But that logic, anything society accepts is an answer. You could just as easily say that society accepting high crime rates is an answer.
You're right that policies often reflect public opinion, but when we're debating policy ideally the conversation would go deeper than that. Public discussions about policy in the open, on forums, etc, is a big part of how public opinion gets formed, and those discussions should probably dig into underlying goals and identify the costs and benefits of different approaches beyond just checking what the current majority preference is. Things can get a little circular when being popular is the justification for why something is popular.
Also, you used "begging the question" properly! I'm weirdly refreshed by that having just seen it misused in another comment.