Last time I looked at data about this, it appeared that even a poor father who was present was better than no having a father in the home. If I remember right it was measuring the likeliness of a teenager to end up in prison. If there was a segment of fathers that were worse than not having a father, I don't think it shows up in any study I've seen.
Gilder's Wealth and Poverty book cites a lot of studies and examples showing how society has changed in ways making it harder for dads to stick around with everything from how drug policies are enforced to the way that welfare resources are allocated.
I think their point is that those bad fathers don't show up, because they don't care about their children.
Are you doing something other than assuming that 'caring' is the primary factor?
Even if this would be the case, we should allow those fathers to spend more time with their kids. For example, it is very difficult for a man to find a part-time job. Most companies take "I also want to spend some time with my kids" as "I don't really care about the work I do". You can care about the work without wanting to devote your entire life to it.
You're looking at the drug war, high school graduation rates, ability to find a job, attached to teenage pregnancy, lack of commute options, and below living wage - likely connected to public health issues including water treatment, sewage, inneficient or unsafe homes (hook worms, sceptic, HVAC)
So instead of a 1 time $10k (which is delusional) think marijuana being legal, healthcare and childcare being affordable, public transport - or at least not a food desert in a walkable community, and $15+/hr 30+ hour weeks at a single employer.
But the good of the children is part of why past societies have incentivized keeping parents together to care for their children and maybe we've gone a bit too far in the other direction, away from a happier medium.
Stigmatizing divorce does absolutely nothing to make fathers emotionally invested in their kids. If anything, it can make them resentful of their kids.
The article was about how boys need emotional support from their father. A father who is present and married but still demands that his son "man up" and bottle up every problem is of no help.
Why would you be totally absent from most of their lives?