We did this before in the 80's/90's... the "Stipend to stay at home mothers" was called Welfare, they received preferential treatment in public / subsidized housing and vouchers, free food via WIC, monthly payments in cash, free medical coverage etc

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It basically failed society because instead of empowering women to have skills and gain experiences that could be marketed, they more or less became dependent to remain low income (or lose housing) and have more children to increase income.

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I'm not saying there shouldn't be a much better program then what we have now... but paying people to have kids and stay home historically has not worked well in the US