I actually don't think their logic is that implausible.
Obviously, it's not about giving people more time for baby making.
But (just as an arbitrary example) if you're spending two hours per day driving to and from work, slashing that down to a single hour can massively reduce a family's overall stress level.
And "Less stressed people have more room in their lives for bigger families" is an equation that doesn't sound that dumb.
Obviously, there might be better ways to go about this. Or there actually might not.
There's definitely more impactful ways to improve people's work-life balance, but most of those aren't as easily implemented.
In an ideal world, they might have done extensive studies into why people don't have more babies, and then selected an efficient parameter to tune.
(As a rule, investing into public transportation will usually pay socio-economic dividends either way, as long as it's done at least halfway decently.)
In a less ideal world, massive lobbying by the very people profiting off this investment first might have been involved.
Overall, this whole affair has decent odds of becoming some sort of net benefit overall.
Supplying people with basic life necessities should not need to garner a profit.
This goes for food, water, shelter, but also electricity, healthcare, public transportation, and internet.
(Coincidentally, most of these are basic human rights.)
Society as a whole experiences net benefit (even am economic one) from those, so society as a whole should fund them.
Yes, this requires taxes.