I understand that Scripture is God-breathed and is certainly extremely precious. But who in history came up with the belief that all Scripture is the literal word of God?
I think you're asking the question the wrong way. As far as I can tell, no Christians seriously looked at the Bible as a human work until the 18th Cent, with one 17th Cent exception. There were interpreters both ancient and during the Reformation that looked at the historical background of each book and tried to interpret it in historical context. But they still saw it as the oracles of God (a phrase from Calvin). Here's a comment summarizing Calvin's view:
"When that which professes to be the Word of God is acknowledged to be so, no person, unless devoid of common sense and the feelings of a man, will have the desperate hardihood to refuse credit to the speaker. But since no daily responses are given from heaven, and the Scriptures are the only records in which God has been pleased to consign his truth to perpetual remembrance, the full authority which they ought to possess with the faithful is not recognised, unless they are believed to have come from heaven, as directly as if God had been heard giving utterance to them. This subject well deserves to be treated more at large, and pondered more accurately. But my readers will pardon me for having more regard to what my plan admits than to what the extent of this topic requires."
For him, Moses was the author of the Pentateuch, and he was a prophet, which means everything came from God, though it was Moses' wording. Similarly direct inspiration applied to all of Scripture.
Now in practice he didn't quite hold an extreme form of inerrancy. He understood that OT books differed in a few details (e.g. differences in counts of people) and thought that didn't matter. He understood that the Sermon on the Mount probably was actually a summary of things Jesus had said at different times. But still, he mostly understood the Bible as the Word in a fairly direct form.
In the next generation after the Reformers, some people moved even further in a literalist direction, as a response to Catholic attacks that pointed out that no one could agree on the meaning of Scripture. The hope was that a sufficiently literal approach could avoid disagreements.
But I think the modern view that both of us hold depends upon a kind of critical approach that didn't start until after the Enlightenment. It's hard to look at the Bible and see how anyone could avoid seeing it as literature produced by different authors with different and sometimes conflicting viewpoints. But as far as I know this kind of understanding didn't exist among Christians until fairly recently.