There is a problem with your premise; prior to Ravenna, the capital of the Western Roman Empire was Mediolanum and had been since 286 when Diocletian moved it. Not Rome.

I think your assertion that the identity of Rome or that the Imperial rule was tied to the Papacy is very wrong for this point in time, especially considering the Edict of Milan wasn't even 100 years old yet and Christianity had an awful lot of solidifying yet to do.

The pope was officially the bishop of Rome, and the bishop of Rome is a local office tied to the bishop's see, just like the bishop of Milan, Ravena, or York. Being bishop of the iconic city of the Roman empire gave the bishop of Rome a lot of clout (which increased over time), but he was never the bishop of the entire empire, just the largest city itself. So when the capital moved to various locations in the empire, the bishop of the city of Rome stayed put.

Through time, the bishop of Rome's influence continued to grow relative to the bishops of other large, important cities, leading to the eventual defacto (and then official) place of the pope as head of the (western) RC church. But this took centuries to develop, and in the fourth century the pope was still merely a very important bishop of a very important city.