There was a study that looked at outcomes, but I think maybe it got pulled because every misogynist and Christian/Christian Nationalist bro in the world was citing and misinterpreting that study for a while.
I think there was some question about methodology too, but at the moment I can't recall why I'm thinking that at all.
Whatever.
There were problems with methodology because it made the assumption that single fathers were equivalent to single mothers both in how they became single parents, how hung up on the court system they were (child support, custody, etc), and how much support they received as a single parent ("I should help my son/brother raise his children because at least he stepped up" vs "she should have thought about that before she abandoned their father" type narratives.
Society likes to make children a punishment to women. Not exactly news.