Sure, I'd take a 1.3pp reduction in poverty in the abstract, but this is the larger point I'm making here is that the amount of poverty explained by single motherhood is way, way lower than conservatives tend to claim (even setting aside the fact that zero single motherhood is literally an impossible policy goal). Further, what I argued here echoing Brady et al. is that this poverty reduction would only happen because our economic institutions have a much higher single parenthood penalty than most other countries. There are countries where bringing single motherhood to zero would have no impact on poverty because ultimately, poverty's cause cannot be reduced to the behavior of individuals, since individual behaviors are only one side of the interaction—the other being the distribution of goods in the economy. This is empirically confirmed by Brady et al.'s finding that what country you live in changes the poverty effects of your behavior.
As to whether the paper is "accurate," you can't establish that without actual evidence. You have only raised conjecture here. But it would logically follow that their simulation of the counterfactual accounts for all of the systematic differences between single mother and non-single mother households, which would include crime, the man's willingness to work, etc. since those differences are baked into the differences in poverty rates used for this simulation. It might also be the case that reducing single motherhood would have other benefits not related to poverty, but those have to be argued for on their own terms since single motherhood is not that big of a poverty explanation in the first place.
Finally, the welfare state simply does not by nature of existing in any form disincentivize marriage. There are bad welfare designs that have what are called "welfare cliffs" for when someone gets married, and I think those are bad. I advocate for universal, social democratic welfare models without means testing such as universal child allowance. This doesn't incentivize or disincentivize marriage either way. Even with bad welfare designs, however, there is no evidence that they have increased poverty. The pre-tax and transfer poverty rate has been about the same for the last 60 years, while the final poverty rate (once you include welfare) has dropped significantly in that time. The welfare state is the only proven way to get very low levels of poverty in an industrial/post-industrial society.
