What does it matter whether the Apostle Peter founded the church in Rome or not?
Why is it important that he was the first Bishop of Rome for 27 years?
What part of your dogma is Peter so critical to that without him the dogma becomes meaningless?
All of it.
It rides and falls on the contention that "Peter and his successors" have a connection that allows them to be the final say no matter what. Doctrinal development, custom, everything is attached to this claim of essentially absolute authority.
The Pope is the last "absolute" monarch on earth.