You summarized the paper as, “children from at-risk families achieve better education when the father ends up incarcerated.”

The one study you’re citing here might suggest your summary statement if “parents on the margin of incarceration” was equivalent to “children from at-risk families”. But those are very different concepts.

You can have an at risk family just by being low-income. Certainly many low-income families are drawn into crime, but by no means all, or even a majority, of low-income families, have a parent who is at the margin of incarceration.

I think the only thing you can reasonably conclude from this study is that leniency in the judicial system towards parents just because they’re parents may be misguided.