The legality and acceptability of divorce isn't mentioned but I think it should be. Single parents will be rarer in countries where divorce isn't a viable option but that doesn't mean the children are raised in healthier environments.
Exactly: having to bond with a crazy or abusive parent is what's actually unhealthy, not lacking a parent. Children grow up perfectly fine making bonds with non-parents. (See also the father/mother figure trope.) They may do it even if the parent(s) exist but were not fit for the role. In many countries extended families can help sort this out. It is only a bigger problem if you have a single parent + no extended fam…
Teachers are part of large state institutions, paid workers. They're not going to finance someone's surgery, rent, or groceries. Offloading this kind of stuff onto the state doesn't work well because the situations aren't legible and the type of support required necessitates a great deal of intimacy on the part of the benefactor and a great deal of vulnerability on the part of recipient not to mention a legitimate impetus from both parties to make things right.
I'm restrained in my ability to extrapolate, but from my personal intimate, experiences extended families don't exist in the US. We've built ourselves out of that. And even a couple hours of driving becomes a huge barrier when seeking child care. Let alone half a dozen, and that's in the cases where parents/children aren't estranged which is an increasingly common phenomena. Between that and economy, and economics... Families may well span the whole continent and it's simply infeasible to support one another.