“Everyone knows that the Papacy, like everything else, developed over time”
The Roman assertion is that the Papacy did not develop over time. There was a Pope right after Peter. There was no 600+ years of tying to figure out that there was a supreme and universal pontiff in charge all along.
Peter was a Pope. That doesn't mean that the full understanding of the meaning and significance of the Papacy didn't develop over time. Pastor Aeternus wasn't written down in Peter's own hand and only uncorked in 1870.
Read Newman if you don't understand the concept of development of doctrine.