So Clement laid the foundation for the Papacy. This is exactly my point. Here is the start of the circular logic. After you unwind all of the layers, you end up with one man writing a letter that was rejected from the canon.
Two interesting things about 1 Clement. First, it claims inspiration (1 Clem 63:2). Second it speaks of the phoenix in Arabia as a real bird (1 Clem 25).
1 Clement is not canon for good reason.
I agree that Clement's letter should not be in the canon (the criteria for canonicity are very strict), and I agree that it demostrates the apostolicity of the Papacy. I don't see any circular logic though.