Such systems exist today, at least in Alaska. The GRA is only available to single parents. https://singlemothersgrants.org/single-mothers-assistance-in...
As for the restriction to single parents, I can certainly see the potential for unintended consequences. Paying people not to get married means fewer people will get married — just as paying people not to work, as the "welfare cliff" effectively does, means fewer people will work. I broadly support the idea of helping people who need help, but it needs to be done in such a way that it doesn't tend to trap them in their situations.