That "there is no authority except from God and those which exist are established by God" should give us pause to be skeptical of your theory about the purpose of government. That is to say, yes, this teaching is about preventing "violence, sedition, and revolution against the government," but not only those things. It also gives us direction about what we are expected to do with the "much" we have been given.
I think it's okay for Christians to be involved in government. Perhaps with our influence, we can even help return some degree of compassion to policies that led to nations' abandonment of their people in favor of what's been spun as "economic growth."
But can we find a "firm command" somewhere in the teachings of Christ for us to force unbelievers to behave like believers, against their will?
As someone who has been responsible to oversee exactly that in various circumstances, I can assure you that such a thing only makes people resentful of Christianity, and causes them to hide better, not change. That sort of obligatory obedience to "moral" rules can do nothing to change a person's heart, or spare them from any degree of wrath. Let's instead follow the "firm commands" we actually do have: "Go therefore and make disciples of all the nations," not obligatory followers of "moral" laws.
