Allow me to suggest you read any of the ante-nicean fathers. They cite it as an authority continually.
And, to quote Paul, “”All scripture is inspired by God and is useful for teaching, for refutation, for correction, and for training in righteousness, so that one who belongs to God may be competent, equipped for every good work.”
So, “The Bible Only” as being DIRECTLY from God is a matter that is settled by Paul.
ante-nicene
It doesn't follow from the 2 Timothy quote. No one is disputing that the Bible is inspired, useful in arguments and in training, and it has been used as such by the Fathers of the Catholic Church since the time of the Apostles. What is being disputed is that it is the only rule of faith.
Granted, all Scripture is inspired by God.
St. Paul says Scripture is "useful" he does not say it is sufficient.
And in the context of this quote he is referring to the Old Testament not the New Testament as he tells Timothy: "because from thy infancy thou hast known the holy scriptures which can instruct thee to salvation by the faith which is in Christ Jesus." The New Testament had not yet been penned, certainly not 2 Timothy.
But according to the "Bible Only" principle the Fathers would be a non-Biblical authority, making them useless.