I am adding responses to comments on my postings on both parental responsibility and obesity. I apologize that I do not always do this, but my only excuse is time pressure.
I do not know about the Australian system, but it sounds interesting. Australia has been a pioneer in student loans and other ways, so I am not completely surprised to learn that they have been active in providing parental incentives to improve education.
I do believe that parents are mainly responsible to raise their children, but that is why I am willing to offer parents incentives to give their children better opportunities. Pressure can be placed on parents to induce their children to behave better. My view is that poor parents love their children as much as rich ones, but poverty leads to behavior that is disadvantageous to the children's future. Progresa and similar programs try to offset that.
The fact is that Progresa has "worked" at least in the sense of leading to longer school attendance and better grades at school.
Should parents be punished for children's behavior? Absolutely in my judgment since they are ones who can have the greatest influence affecting their behavior. If parents bring children into the world, why does that not carry with it parental responsibility for various forms of their children's behavior?