It's a tired and untrue cliche, but it persists because it's the comfortable and convenient narrative that allows the bad public policy that is the true cause of poverty and homelessness to continue unexamined--and therefore, unabated.
The United Nations Commission on Human Rights isn't fooled by the American narrative. Take a look at this excellent report by professor Phillip Ralston. Here's some of what he found:
"10. I have been struck by the extent to which caricatured narratives about the purported innate differences between rich and poor have been sold to the electorate by some politicians and media, and have been allowed to define the debate. The rich are industrious, entrepreneurial, patriotic, and the drivers of economic success. The poor are wasters, losers, and scammers. As a result, money spent on welfare is money down the drain. To complete the picture we are also told that the poor who want to make it in America can easily do so: they really can achieve the American dream if only they work hard enough.
11. The reality that I have seen, however, is very different. It is a fact that many of the wealthiest citizens do not pay taxes at the rates that others do, hoard much of their wealth off-shore, and often make their profits purely from speculation rather than contributing to the overall wealth of the American community. Who then are the poor? Racist stereotypes are usually not far beneath the surface. The poor are overwhelmingly assumed to be people of color, whether African Americans or Hispanic ‘immigrants’. The reality is that there are 8 million more poor Whites than there are Blacks. Similarly, large numbers of welfare recipients are assumed to be living high on the hog. Some politicians and political appointees with whom I spoke were completely sold on the narrative of such scammers sitting on comfortable sofas, watching color TVs, while surfing on their smart phones, all paid for by welfare. I wonder how many of these politicians have ever visited poor areas, let alone spoken to those who dwell there. There are anecdotes aplenty, but evidence is nowhere to be seen. In every society, there are those who abuse the system, as much in the upper income levels, as in the lower. But the poor people I met from among the 40 million living in poverty were overwhelmingly either persons who had been born into poverty, or those who had been thrust there by circumstances largely beyond their control such as physical or mental disabilities, divorce, family breakdown, illness, old age, unlivable wages, or discrimination in the job market.
12. The face of poverty in America is not only Black, or Hispanic, but also White, Asian, and many other colors. Nor is it confined to a particular age group. Automation and robotization are already throwing many middle-aged workers out of jobs in which they once believed themselves to be secure. In the economy of the twenty-first century, only a tiny percentage of the population is immune from the possibility that they could fall into poverty as a result of bad breaks beyond their own control. The American Dream is rapidly becoming the American Illusion as the US since the US now has the lowest rate of social mobility of any of the rich countries."