No, I'm not starting a conspiracy theory about a secret manuscript of Romans that has been zealously guarded by generations of fanatical monks. It just seems to me that logically something is missing in Romans 13. The other times that Paul makes an exhortation to part of society, he balances it with exhortations to the corresponding part of society. Children, obey your parents; and parents, don't exasperate your children. Husbands, love your wives; and wives, obey your husbands. Slaves, obey your masters; and masters, don't forget you have the same master in heaven. So why does Romans 13 exhort people to obey the government, without an exhortation to the government to govern well?
I'm guessing Paul felt he had to leave that implicit, Christianity was already being suspected of subverting the Roman Empire. But he does give us a challenging picture of what government ought to do, right there in the exhortation for citizens to obey the government. Verse 4 says the ruler "is God's servant, an agent of wrath to bring punishment on the wrongdoer." So the exhortation to the government would be "act against those who do wrong, not against those who do right." He might also have added that rulers ought to be humble. God placed them in authority to be instruments of His wrath. They should not think they are irreplaceable. God can remove them and put in other authorities if they don't do what is right.
On this day before election day, I'm thinking we citizens ought to understand both sides of Paul's exhortation. We are ordinary people, who ought to obey the government in our daily lives. But in our representative democracy, we are also the sovereigns, who get to choose who will be the authority for the next four years. May we choose wisely. May God show us the truth about the two candidate, and may we be wise enough that the truth matters to us.