JP, at some point you are going to have to tell us what it is that you are talking about with regard to how to 'fix' the system whereby separated parents support their children. You seem to keep saying that the way we address the issue now is bad, and that you would have us stop addressing it that way, but you haven't said how you would address the issue.
I understand, you say it is best for the family unit to take care of the children, or decide how to take care of the children. Well, of course that's the case - but that doesn't have anything to do with how the government manages the conflicting interests that arise when families choose that they don't want to do that - that they don't want to act as a unit with regard to taking care of the children. That is one of the most important things that government does, it provides means of resolving situations in which citizens have conflicting interests.
It almost seems like you want to make it illegal for people to separate. I'm guessing that's not the case, but your lack of even the most basic mechanistic plans for achieving your goals, leaves me unable to figure out what it is that you would like to do. Effective governance is more than laying out goals or stating how things should be - it is implementing policies to help get to those goals and to help make things the way they should be.
So, when parents do not want to be together anymore, and they can not agree among themselves how to financially support the children, what do you propose the government do? When those conditions aren't present, there isn't much need for the government to be involved. But when those conditions are present, then there has to be some sort of government involvement to resolve the conflict between the parents. Basically, what you have said is you don't want those conditions to be present - you don't want there to be a conflict between the parents. Well, that's fine and dandy, but the reality is that there sometimes are conflicts between the parents, your wishes to the contrary notwithstanding. Unless, of course, you are asserting that the government choosing to get involved and provide a child support mechanism is what causes all of the conflicts to begin with - that without that, there would be no incentive for parents to have a conflict, and thus they'd always be able to agree (or would just stay together). Good luck selling that notion.
So, again, when parents can't agree on how to financially support their children, what should government do? Nothing? Take the children from them? Fine them $20 a day until they agree on something? Lock them in a room until they agree? Take away their cookies and send them to bed without dinner?
Seriously, you've been saying you would fix this for a long time, if you could get in a position to do so. Surely by now you have some idea how you would go about doing that - other than that it would be different than what we do now.
Who knows, I might support your ideas - when you give me the slightest clue what those ideas actually are.