Labeling a team pro-G is similar to labeling pro-lifers anti-choice. Or pro-choice people as pro-abortion. It using one sided proposed narrative to create a caricature of the other.
It's a very common stereotype on the right, that members of left are interested in more government for the sake of government. And labeling a side pro-government perpetuates this misperception.
Given that, I'll grant that it's probably a mistake to think that people's political ideologies have anything to do with a theory of government at all.
Most people's political ideologies are probably about as refined as a blue/red color preference.
It's a very common stereotype on the right, that members of left are interested in more government for the sake of government. And labeling a side pro-government perpetuates this misperception.