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.
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 family support. I imagine social services (is that what they're called) or teachers compensate for the extended family role in countries like US?