I don't really understand why they need the entire work to be infallible. Different writers, different time frames, and different needs. I would find it more interesting to see if the same author contradicts himself.
You have to understand the literalist chain of thought. There is no evidence to support the more extraordinary claims of the Bible; frequently those claims
contradict evidence. They need the whole thing to be divinely inspired in order to believe any of it- and they're already emotionally invested in believing it.
Their entire personal identity is wrapped up in this idea of being "Saved" by the blood sacrifice of Jesus. To believe that he died and rose from teh dead, they need to believe that the entire work is true. They need to believe in Original Sin in order for there to be a debt to be paid; they need Genesis to be completely true in order to believe in Original Sin.
If any part of the Bible is wrong or even just a metaphor,
any part of it could be taken the same. If Genesis is metaphorical or wrong, there is no Original Sin, ergo no salvation.
Liberal Christianity is far more flexible, but for literalists, their need for the entire Bible to be literally true is deeply ingrained into their personal identity, sufficiently to ignore or rationalize any actual contradictions in teh text.