There's another aspect of this, that escapes some people. Part of the problem that resulted in folks leaving England a couple of hundred years ago was the spectre of debtors' prison, where some were incarcerated simply because they owed money and couldn't pay.
Now if one can't pay his child support (note that there's no differentiation in the law as to whether he can or will), he goes to jail. But the law says not because he "owes the money," but for "contempt of court."
That's changed. Now they send them directly to jail for owing money. Arguments re: debtors prisons, slavery, indentured servitude ... all been raised. Courts insist that fathers have no constitutional rights, therefore can't find that any rights have been violated.