Well yes, they don't predict the future, since that is not something that's possible to do with accuracy. However, even if you were to make the case that the decline in poverty would be greater in the future, you'd still be advancing a weak argument, since we know how to decrease poverty way more. We know that single motherhood is not naturally a risk for poverty. It's entirely dependent on what economic institutions you build. That is the fundamental point of Brady et al.'s argument.
With regard to your welfare argument—I'm not sure what you've read about welfare, but giving parents the same amount of welfare is the norm in rich democracies. It's called a child allowance. You give every kid a check every month, regardless of income or whether their mom is married. We've halfway implemented this (though rather clumsily) in the advance child tax credit that's gone into effect this summer. This is by far the most preferable way to handle the issue because child poverty in particular is driven by the fact that children are humans with material needs but who do not bring in any income. A universal child benefit of $300/mo that replaced the current CTC would cost barely over 1% of GDP—extremely attainable.
As for the question of marriage—ok, I think what you've established is that such a benefit is marriage neutral. It fails to punish you for getting married, but it does not actively incentivize you to get married (or, inversely, punish you for being unmarried). But to me, this is a good thing. The purpose of anti-poverty policy is not to try to push people into marriages, it's to get very low poverty. Poverty is its own evil. If you can drive it very, very low with very straightforward policy (which you can), that is by far the best option.
If marriage is a good in itself, which I believe to be true, why would our strategy be to whip people into marriages with the threat of material deprivation? This seems incredibly perverse to me, because there is no way of avoiding the fact that by doing so you're almost certainly pushing many people into ill-advised or even abusive marriages that people feel compelled to enter because they risk poverty otherwise. Single motherhood is very materially (not to mention spiritually and emotionally) difficult in the present economic environment, but this "disincentive" doesn't seem to have actually driven up marriage rates. The inputs for why people get married or not are far, far more complicated than the inputs for why people are poor. Poverty is a single dial called "income"—marriage is a veritable flight deck. I think increasing marriage would require cultural change that can be helped by living the example of good and life-giving marriages in the world. I don't think the way to push marriage rates up is to withhold food from children. As harsh as that sounds, that is what "single parenthood disincentive" amounts to.
