Longer sentences mean more prisoners and more prisons. Check out the ongoing US experiment.It means weak sentences for crime, particularly violent crime. Sentences for that type of crime should be much stronger and recidivists locked away for much longer.
If sentences were longer there would be less strain on prisons.
Violent crime has bugger all to do with poverty, it is a choice.
I suspect there are courses available to prisoners, I have certainly read about prisoners completing degrees and educational courses while in prison but I doubt the majority are interested, certainly not the gang members that make up the majority of inmates.
Agree with mental health, totally neglected, prisons aren't the answer for that problem.