Israel is God's portion and as such, God alone is ever the king of Israel. David being a man after God's own heart, was allowed to rule temporily. God has taken it back and Jesus occupies the throne. No one rules Israel other than Jesus, since Jesus. Peter was given no earthly throne, nor was any other apostle or disciple. Moreover, Peter was never an apostle sent to gentiles, so he would have no work in Rome. Paul was that emissary.
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Sound reasoning. Sound historical facts.
Not only that but the lesson from the bible of what happens when the people clamor for a king or a prince or whatever over them, should be enough to give people pause.