–“So we **do** need a government?”–
We need a market for the production of commons. And we need a legal system. Whether we need government is still unsettled. But I would argue ‘no’.
–“So it could still be privatized society, but we need to apply new laws to promote cooperation, trade, and prevent parasitism.”–
Correct. One law, natural law, total prohibition on parasitism: physical, verbal, and by externality. A market for the production of commons. And as far as I know there is no ‘government’.
It is useful to have a state department that foreign nations try to negotiate with.
But even this is better conducted in public.