In reality the idea of Scriptures being "inspired" is only borrowed from the phraseology of 2 Timothy. When the canonization process was invented, the idea that any of the Scriptures were "inspired" as now understood was foreign to Judaism and Christianity.
The very first suggestion that this "inspiration" meant a source of theological revelation came neither from Jews or the early Church, but from the gnostic teacher Basilides. By the second century, the Church had already developed a liturgical calendar and had begun celebrating the Eucharist preceded by a series of readings based on the yearly synagogue liturgy. Instead of two readings (one from the Torah and one from the Tanakh with the chanting of a Psalm in between) as done by Jews, the Christians added the "memoirs of the apostles" as a third reading, to use the phrase coined by Justin Martyr.
From these "memoirs," Basilides created a series of "proof-text" arguments in support of Gnosticism. The Gnostics held that hidden knowledge came from studying written revelations, and Basilides held that Matthew, Luke, John, and some of the Pauline epistles were thus "inspired" as Gnostics believed.
But it would be the bishop-turned heretic, Marcion of Sinope, who would take Basilides arguments and turn them into the means to create a "canon," or rule for declaring that the writings themselves consisted of a revelation. Up to this point the only revelations believed upon by Jews and Christians were the theophanies to the Patriarchs and the Great Theophany at Mt. Sinai, the oracles to the Hebrew prophets, and (for Christians) the Epiphany in Jesus Christ. The written Scriptures themselves were not equal to these revelations of G-d.
But Marcion saw things differently. Setting up ways for determining "inspiration," Marcion created the "rule" (in Greek, the word for "rule" is "canon") to create a library of texts from which to promote salvation via "gnosis" of study of the written texts. His rule or canon rejected the Hebrew Bible entirely, and by 130 CE had a collection of canonized texts that included an edited version of Luke and some of Paul's letters from which Marcion had removed any information of Jesus' suffering or any suggestion of the Incarnation.
After Marcion's excommunication, the Church decided to look further into the claims of Basilides and Marcion. However, instead of seeing the written works as primary revelations in and of themselves or equal to the theophanies of old, Church leaders saw in the texts an additional form of revelation to add to the deposit that already existed.
"Inscripturation" would be a late invention following the Reformation, however. When the early Church began to speak of a canon of Scripture assembled by its own authority, it searched not for the earliest texts but sought to consider the liturgical collection of "memoirs" read prior to the Eucharist. What was received was not as important as what was in use because the texts that became part of public prayer were seen as written under the influence of Holy Spirit more so than those that were merely popular and read privately outside liturgical settings.
In unison with Eusebius, Athansius would give the first complete official sanction of the 27 books of the New Testament in his famous Easter Letter of 367, stating: "Let no one add to or take anything from them." His decision would be ratified in Hippo Regius in 393 and Carthage in 397 before finally receiving recognitio from the pope in 405. It was not the originals that were considered the most authoritative but the forms each book took by the time the canon was closed in 367 that marked the end of any fluidity. Up to that point any redactions made were considered part of the "inspiration" process by the same Church authority.
The idea that the texts in their most basic form are responses from the Protestant era. Unsettled with the paradox of "Sola Scriptura" being based upon a canon settled by Papal and other Catholic authority, some Protestants developed a theory that rejected the idea that any authority but that of the popular church moved by the Spirit had anything to do with settling the canon. This would introduce the theory of inerrancy and claims that the earliest writings (before any "catholic" liturgy employed them) of the New Testament texts consisted of word-for-word dictation from a "God-breathed" process. Anything after that was heretically introduced and soiled the written Word, they claimed.
The idea of "Inscripturation" is held only by a minority that rejects critical and source reconstruction study of the Scriptures, limited to conservative Fundamentalist movements. It is viewed as incompatible with the historical development of the canon, inconsistent with the textual evidence, and intellectually dishonest by the majority of Biblical scholars and exegetes today.