Ethics aside, that is the problematic part of your reasoning. First, only less than half of treated patients relapse [1], second: a relapse is not a measure of a failed treatment as it is a qualitative value (relapse happened/didn't happen), not a quantitative one (to what degree did the patient relapse into old behaviour).
More importantly, it most probably costs more to incarcerate patients than to treat them. The US has the highest incarceration rate in the world. Thats expensive: $47.000 per inmate per year. [2]
People often confuse addicts who refer to themselves as addicts for life, which is a useful psychological technique to avoid thinking that can lead to relapse, with the idea that addicts are incurable. It's unfortunate, but a bit of education (like your comment) goes a long way toward solving the problem.
Ethics aside, that is the problematic part of your reasoning. First, only less than half of treated patients relapse [1], second: a relapse is not a measure of a failed treatment as it is a qualitative value (relapse happened/didn't happen), not a quantitative one (to what degree did the patient relapse into old behaviour).
More importantly, it most probably costs more to incarcerate patients than to treat them. The US has the highest incarceration rate in the world. Thats expensive: $47.000 per inmate per year. [2]
[1] = https://www.drugabuse.gov/publications/principles-drug-addic...
[2] = http://www.lao.ca.gov/PolicyAreas/CJ/6_cj_inmatecost