The answer isn’t binary, there is room for both carrot and stick. Saying that, I agree that the seeds that grow crime must be eradicated - no/shit parenting, lack of values, lack of community, PC aversion to challenging cultural crap, mass cowardice in refusing to challenge poor behaviour and say no.
Very true, in certain communities parenting is virtually zero with Women having numerous children with numerous men who more often than not have zero influence or support for the child. Put this down to where feckless slags know that the state will support them and their offspring with over generous benefits. FFS various birth control methods are given out free, so there is no need for this.
IMHO Prison initially should be a punishment & not just a curtailing of someone's liberty. Initially Prisoners should be OBLIGED to work a minimum of 8 hours a day, either in a simple workshop, chain gang type work on farms, road cleaning etc & every prison should have a modified version of this which could be adapted to generate electricity which if not required at the prison, sold to the national grid.
By keeping their nose clean, doing the work, prisoners could qualify for certain privileges, watching TV, access to small luxuries like sweets etc. Once a time on this labour is reached, specified by the judge, the prisoner becomes eligible for training in a suitable trade, plumbing, electrician etc to help rehabilitate him for the outside world, any infraction & its back to the treadwheel until he learns the errors of his ways!