how does it make any sense to blame her parents who are the products of the exact same structure she is now struggling against?
If the point of a system is process then you have the classic "the bureaucracy is expanding to meet the needs of the bureaucracy" situation. At some point you need to look at output.
Each of those children, knowing only their own lives, may grow up to have n-more children that they can't afford. Is it suddenly their fault, or is there a bigger, vicious cycle of poverty at play here?
The blame lies with the society that refuses to help impoverished children break the vicious cycle. Most of the people who deride the need for these kinds of services have never even exchanged words with somebody that poor, let alone been in that situation themselves. They have no idea.