Wouldn't it be nice if U.S criminals in exchange for their records erased agreed to accept refugee status, immigrate and begin life in new

Not really.
That's just passing the buck so that they become someone else's problem.
Much more effective to explore the means of rehabilitation.
There are three models I've heard of that have an 80% success rate.
One is a Vipassana meditation program run at India's worst prison for its most hardened convicts.
Another is Greenland's system which seeks to educate, build self-esteem, and teach work skills during gaol (jail) time.
Another is a new pilot program in Australia which is run by psychologists working with convicts on parole to train and place them in jobs and help them adapt during their first two years out.
I reckon a system which combined all three would be even more effective.
Governments often seem to think such programs are too expensive (the Vipassana is free) - but they forget that preventing people from re-offending would save a lot more than is spent on the costs of crime to society and the costs of justice.
Running programs to save young people at risk before they become offenders would make a lot of sense.
Look at the causes.
Prevention is better than cure.