I think I can see a way to come to a compromise here.
One of the main ways, if not the main way, for a person to have a disadvantaged start in life (and, consequently, a disadvantaged life) is being brought up by parents who, for one reason or another, either can't really cope with having kids or simply can't be arsed with them. It could be all sorts of reasons - drug/booze problems, mental issues, demands of work, ill health or other things (many of which will be an inescapable result of the parents' own upbringing, and so on, ad infinitum). Or the effects of falling in with 'the wrong crowd' could be so bad as to undermine the efforts of well-adjusted, conscientious parents. So by the time a kid brought up like this reached adolescence or early adulthood, the damage is done.
So one way of trying to level the playing field is to try and instill in people who've ended up in this situation the values a well brought-up person takes for granted: the idea that it's good to do Good and bad to do Bad. Very often, people who are consistently in trouble with the law have very little by way of knowledge or skills, so as I mentioned earlier some kind of education or training should be an integral part of rehabilitation - and along with that, there has to be something to demonstrate that there are limits to acceptable behaviour and that society will not tolerate infractions of these limits; in other words, a punishment. In other words, I think it's better late than never to try and turn someone into a functional member of society.
If you treat people as irresponsible and lazy, on the basis that they can't help but act like that due to circumstances beyond their control, how are they ever going to be anything else?