I don’t accept your claim that Rome is unique in that way. Although James is generally considered the first Bishop of Jerusalem, Peter was head of the Church at Jerusalem before leaving James behind. So I think it would be fair to say Peter was Bishop of Jerusalem, and it is universally accepted that he was Bishop of Antioch. Paul visited and was involved in key events in both those cities.
The main things that distinguish the See of Rome in the history of the papacy are that it is the most recent see, and the longest-lasting see, of the Supreme Pontiff. Those don’t seem like binding precedents that would prevent a future pope from vacating the see.