In that case the welfare is for the kids, not for the parent. i.e. the number of kids is more important than what their head of household is earning.

Welfare is mainly intended for children and the elderly because we don't want child laborers.

A person with no skills wouldn't be able to support themselves regardless of the number of kids.

And I suppose that's ultimately the problem: through a combination of technological advances, which automate much unskilled labor, and a broken incentive structure in many social welfare programs, which disincentivize investment in human capital (because of the "benefit cliff"), a larger and larger underclass of unemployable[0] people grows.

[0]: meaning, the economic value of their labor output is less than the minimum cost to employ them.

A person with no skills that works 40+ hrs a week should be earning enough to live on.

Perhaps. But a person with only one kid? Doing a job that the company needs to have done, even if no great skill is required? If that person doesn't make enough for food and rent, then I repeat, it is the company that is on welfare.

You came up with an extreme example that virtually never happens as a counterpoint to something that is ubiquitous in modern life. This behavior is why people don't like this forum.