Experience with primarily being around decidedly working-class people?
If they put it into savings, their mental health would generally go down the drain, which would screw heavily with their ability to turn up for work, which would put them in even worse of a place. I've seen this happen. Note that studies show that the poorer you are, the more likely you are to be depressed - many attempt to escape from that feeling of pointlessness and having no future with alcohol, drugs, gambling, television, and so on and so forth.
The overuse of scratch cards is just one possible manifestation of an underlying problem - that these people usually don't have the support they need to get out of their situation. That they're living paycheque-to-paycheque with no end in sight, whether they were to save $20 a week or not. And it turns out giving them the support they need is rather expensive.
Also, proper education is incredibly expensive and inaccessible to many (night classes or long-distance learning need serious dedication and motivation with no guarantee of a job at the end of it - a well-known recipe for something that poor people are generally just not good at), and on top of that, many people just don't have the skills they'd need to succeed in further education.
My opinion? The actual issue is that there's little career progression or practical training available to get an employee from e.g. retail shift worker to somewhere else in the company with a near-guaranteed job at the end of it and full pay the entire time. And there's no reason for businesses to create those pathways so long as they have no responsibility to their employees.