So the solution that will lower the use of welfare is to provide facts? So first provide information, then are the people still free to choose or do you have new rules for welfare?
I think there are already a lot of active educational efforts of this kind that aim to help women create better futures for themselves. These include educational programs and job skills as well as family planning help. Implementing more is expensive, so I am not sure how much more we should pursue when funding is scarce.
The key to helping people help themselves is anything that helps them believe they have real power to get beyond mere survival. The people who get stuck receiving assistance for long periods either have major problems or simply have no pathways to success that appear walkable. Those who believe in a better future will generally take that path, but those who feel crushed by their failures will often balk. Those who are broken have a hard time seeing hope.
Most of the moms that posted here are not stuck in such a cycle of hopelessness. Most people who post on Mothering.com are actively building a good life for their children, which is why they are interested in learning about nurturing natural parenting methods. That doesn't match up much with "generational" welfare recipients. While you may think fraud is common, or you may think even that bad character or laziness is common, I doubt it is common here. However, there are many members who do receive some kind of assistance.
To go way way back to the original post topic, if I were to meet a woman who is a SAHM and also receives some kind of assistance I would have no reason in the world to think she has been an abuser of the system, that she has or will be in the system for many years, or that she is making a bad decision that takes advantage of others. While there may be people who "ought to" bring more personal responsibility into their lives so they need less help, I have no reason to think that anyone who is a SAHM is that kind of a person.