Ultimately, the government ought to be designed to help people as they are, not as they should be. Sure, there are some elements of "poor culture" that make matters worse. But the simple truth is that the poverty cycle exists. In the United States, your class is determined almost entirely by your parent's class. Economic mobility is one of the lowest in the developed world, with only the United Kingdom being worse.
Saying "Well, these poor people ought to just change everything about their lives and become exceptional human beings" isn't really a valid response. As Dharma pointed out, that is the instinctual response of the privileged class, because they've never faced any real hardship and have no f**k clue what it takes to get these opportunities when they aren't simply handed to them. Such people will harp about hard work while ignoring the fact that they've never actually worked in their lives. They don't even know what work is. There is probably nothing worse than a person who doesn't realize the incredible advantages they have been given - I would never be so arrogant to presume that I understand the plight of those people who are born into families that have been poor for generations.
Look at how human beings develop. The first five years of your life, you are 100% dependent upon your parents. These years are absolutely formative. Many, if not most, of your predispositions, inclinations and attitudes are developed in these years - so if you have shitty parents, if your diet is terrible, if you were exposed to drugs or alcohol in the womb, if you experience violence and fear, you will probably be damaged, forever, through no fault of your own. Only a very tiny fragment of the population is able to overcome these disadvantages, and so why on earth would the government design policy around them? It makes no sense.