You are correct. This is one of St. Paul’s sweeping generalisation (”all have sinned and fell short of the glory of God” is another). A thinking reader would, however, realize that IF a prince IS a “terror to good work” then such prince is not acting on divine authority.
+Paul is simply saying that rulers received divine authority to punish bad, and reward good work; in other words work that is beneficial or detrimental to the society, not work that makes you holy or unholy.
The fact that our government makes killing of unborn children "legal" makes our government what? Satanic? Why would the Holy See have diplomatic relations with a satanic government?