The logical failure would be that the authority of scripture alone is not scriptural.
Sola scriptura fails its own test - it is internally contradictory, self-contradictory.
The book’s approach is a corollary - scripture contradicts sola scriptura.
Then Christianity crumbles from failure of its own structure.
Whatever the limits of the Truth, it must be self-consistent within; by definition and its own teaching, anything not consistent with the Truth isn't.
Tradition has proven itself inconsistent too often to be presumed correct from mere declaratory inclusion. That leaves Scripture as the only well-delineated bastion of Truth, whether or additional truth is contained therein. If inconsistencies - real ones, not perceived as such by sinful flawed minds - are found, they must be excised. The exercise has left us with the book we have; should more be removed, we have but dust left.
1Jn 5:13 These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God.
We know we have eternal life based on the authority of what was written by John the Apostle...
You could not be more wrong...