Not sure how you got there. What is selfish is to reap benefits without contributing to the work in some way.
It's not an opinion that in many places without a social security system of some kind, people have children because if they don't, they will have no one to care for them or help them. Your family is what you have, and choosing to have no children has serious consequences in those circumstances.
It's the nature of human society that we aren't independent. As we age, or if we get ill, we all need the help of others. We need other people to maintain the basics of society as well. That means as we get old, we need younger people.
The reason that wealthier countries with more social infrastructure have lower birthrates is because the problem doesn't exist in the same way. People pay into social security and other forms of infrastructure, even pensions, and can draw on those resources as they need them. Particularly, as they age, younger people take over those tax payments and also do the work of directly maintaining society and actually caring for the elderly. Even those with no children.
But here is where there is a hitch, because if we consider that children are the private responsibility of parents, in terms of costs and the actual work of caring for them, it means the parents are taking on all the costs, risks, and work related to child-rearing. But the benefits of that investment are going to all kinds of people who have invested nothing.
That would clearly be unfair, which is why we redistribute social funds toward the needs of children in various ways. What often isn't really managed though through our social infrastructure is help with the hands on element - child rearing was never really meant to be done by just the parents, it doesn't work well. It's an activity that requires direct social supports of some kind, for example through an extended family.
As far as I can see this idea of non-related households is taking the idea that all adults have a social obligation toward the next generation and imagining what it would look like if instead of redistributing it through a hands off state run program, it was integrated into the family structure. Which is quite an interesting idea, it would be a much more integrated approach where people understood their interdependence, which can easily be hidden when it's all just the state redistributing your taxes.
I don't think it would supplant the biological family though, I just don't think that's likely or particularly desirable. But there are a lot of other reasons to think the nuclear family may be on its way out.