I'm sure everyone is aware of the importance of fathers being in their children's lives, but usually this discussion (at least here) revolves around family court reform and things like that.

How important do you think marital stability is in general though?

This paper uses US census data and strongly supports the view that traditional family arrangements are beneficial not just for children, but for communities and families as well.

I'm not sure what the author's political affiliation is, but this is probably something that a conservative would enjoy quoting from to support their family values arguments. In particular, the removal of the father causes a breakdown in traditional (almost what you'd call "patriarchal") gender roles which actually appear to be beneficial for families, communities, and children. You can think of it like the mother being forced to take over both feminine and masculine gender norms. And generally failing at "being a man / father" for her children (while also straining to try and be a good mother because of the increased workload of taking on both roles).

The parenting contributions that fathers make have been identified by psychologists to be important for the mental wellbeing of both girls and boys, so this goes beyond things like financial stress, and into the realm of things like discipline, and gendered differences in parenting strategies (for example it's usually the father who serves as a role model and teaches his children responsibility, self-discipline, and right from wrong, among other things). This interpretation is based on good data and what appears to be quite a bit of collaborating research.

You can read the paper here:

https://www.ojp.gov/pdffiles1/nij/grants/206316.pdf

And some key excerpts here:

https://np.reddit.com/r/Male_Studies/comments/ocd3bh/the_effect_of_father_absence_and_father/