Perhaps there is something about the environment of an economically disadvantaged household that could be improved by a stipend which allows at least one parent the breathing room to dedicate full time attention to the child instead of a job (or multiple jobs). I don't think the findings you mentioned cut against that idea at all.

I hear you saying the benefit of dedicated caregiving for children mostly helps families with less economic advantage. I'd agree with that, and suggest that OP's proposal capitalizes on exactly that. I'm not convinced of what may be implied in your argument that low-earners make for bad parents and that children should be separated more from their parents for their own good. Let the internal dynamics of a family be solved first, before saying we need to separate parents from children more.

Moreover, those with more economic advantage are unlikely to take a stipend in exchange for staying home. That's not a good deal when keeping the job pays so much that they can afford to pay for childcare.

It is precisely those with less advantage who will take the deal.

So I don't agree with your prediction that such a stipend mostly benefits those who are already well off.