Let me rephrase: To solve the problem of recidivism, you'd have to suppress records. Most companies have blanket policies to not hire and/or to fire anyone who has any LEO interaction.
You could educate the next Dr. House in prison and it won't mean jack if no one will hire him.
That's the trade space
You could suppress records. Or, you could incentivize retraining and hiring of convicts through programs like tax breaks, job matching, etc. Match the rehab program to the crime, instead of lumping everyone together in a general population. Things like that.
The best solution probably involves some of all of the above, while still upholding the need to prevent sex offenders from working in daycare centers, etc.