Why not simply pay the homemakers? Why is it so important that everyone produce economic output at the widget factory?

Allow me to translate into a language you can understand: The people who are all “unemployed” are actually performing valuable services like maintaining the future labor pool, learning how to become skilled workers, and so on. These people should not have a second job, they should be paid for the valuable services they’re providing.

IMO, basic income for parents is absolutely a policy that Japan should enact.

And the question of how much the payment should be has a straightforward answer: adjust until the birth rate reaches replacement.

If the payment ends up high enough that some mothers or fathers opt to leave the labor force to focus on raising their kids, then so be it; that's probably healthier for society in the long term.

It would be expensive, yes, but cheaper than the alternatives. And anyway, Japan's stagnant economy would likely benefit from the boost to consumer demand.

Sounds good. You're welcome to pay those people as much as you like. No one is stopping you.