Federal or State Run Rehab Centers Built like Jails - Would this work?

So it’s a common and very valid complaint that our country has privatized the prison system and filled it with millions of non-violent drug offenders. These privatized prison systems make huge profits, carry insane lobbying power in Washington, and probably aren’t going to let anything happen to kill their profits.

Why, though, can we not have these same companies build state and federally funded rehab centers (or convert current jails) designed only for non-violent drug offenders? They would be setup essentially like a jail, in that they are mandatory and not fun to be in with cells, etc., but the people in them would be subjected to mandatory counseling, drug education, etc. to help them with their issues. They would have strict rules on violence, in that if you commit acts of violence, you're moved to real jail.

The courts could, instead of laying down massive punishments for these offenses, sentence the folks to mandatory rehab if they plead guilty to smaller misdemeanors. Repeat non-violent drug offenders have a 2nd, even longer stay, and so-on, but never huge felonies on their record. It would cost the same to the tax payer in the short term, BUT potentially far less in the long term. These non-violent people going into regular prisons get institutionalized and their lives ruined by ridiculous felony charges that prevents them from ever getting a good job. This creates a cycle of criminal behavior in this country.

Basically, build rehabs that are similar to jails (or convert current jails into this), but with an entirely concentrated population of non-violent drug offenders with the goal of cleaning everyone up. They would plead guilty to lesser charges to receive this sentence so they don’t have felonies ruin their life.

I'm not talking about smugglers getting caught with a truckload of cocaine or heroin either. Massive distribution of addictive narcotics should not be a rehab worthy punishment, but real jail.

Why hasn't this been done? Would it not work and cost the same in the short term and less in the long term?