In the whole Atlas Shrugged there's hardly any mention of a reason for the existence of a Government.

Other than a couple of words from JG speech, did you find any other?

Did you notice how slim his explanation is? Specially comparing it to the totality of the novel where JG not only does NOT speak in favour of the existence of a Government, but he, and his colleagues acts on the completely opposite way.

There are no contradictions. So...