The Catholic custom is that Peter was called the gigantic Rock long before the Holy Spirit was breathed into him...Mat. 16:18, John 20:22...So your theory doesn't hold water...Peter was called the rock before he was the rock??? Nope
The real churches are based on what was revealed to and taught by Paul the Apostle...
Neither Peter nor Jesus left any instruction on how to build the churches...That was given to Paul...
Peace in Christ