There's no need for a basic income to be set so high that it subsidizes infinite children. If the BI for a family of four was $25,000 in today's money for example, any more children than two would be as financially uncomfortable as it is today.
The key to basic income is to make the amount paid enough to live, but not to live well. The more basic the income becomes, the less incentive it creates not to work. In addition we have more people who want jobs than there are jobs available in our current economy. We can tweak the numbers without wrecking the whole system.
You have it backwards. Most industrialized countries are below the replacement rate even with current monetary incentives (e.g. tax breaks) to have children. Kids are an enormous financial burden to parents, and financially they benefit the wider society, not the parents. Assuming you don't want social security (or its equivalents) collapsing, you want to incentivize having children at least to the replacement rate.
I keep hearing about social security collapsing without more children, but I don't see how adding more people helps unless they contribute some production. Having more kids that will, 30 years from now, wind up unemployed or doing some unproductive job (let's say dog psychologist) not only doesn't alleviate the burden, it even makes it worse. Is "dog psychologist" really useful to society?
If your choices are "30 years from now, I'll have to support myself" or "30 years from now, I'll have to support myself and 2 unemployed kids living with me", what do you pick?
I think the problem might solve itself anyway. What old people will need in the future (as they do now) are goods, services and care (they'll need food, shelter and medical care). Traditionally, kids provided these to their parents in their old age; who grows their own food anymore? With all the increase in automation we're seeing, old people need their kids less and less, if someone else gives them food and care anyway.
It's interesting that there's another HN article talking about the benefits of a four-month paternity leave - https://www.facebook.com/tstocky/posts/996111776858 I seem to remember that one of the reasons Europe has longer maternity and paternity leave is because of the need to increase birthrates post WWII.
The key to basic income is to make the amount paid enough to live, but not to live well. The more basic the income becomes, the less incentive it creates not to work. In addition we have more people who want jobs than there are jobs available in our current economy. We can tweak the numbers without wrecking the whole system.