If we could achieve desired results by doing so then should we still not based on the false assumption that $500/month will make everyone lazy?
The idea behind it is to mitigate the symptoms of poverty. The goal is to improve the quality of living for everyone in a given society by improving financial stability and mobility and in turn health, happiness, a sense of community, safety, and productivity.
If it helped a single mother focus more of her time raising her children which resulted in those children being better able to acheive their potential and produce more in their lifetime (escape the cycle and life of poverty), does the 'problem' of her not working, even temporarily, justify letting her, the child, and later society suffer?