Christianity, the historical religion, does not make the claim that the Bible is the infallible Word of God, so I don't really see a reason (as a Christian) to spend time hypothesizing about if it were.

That said, there certainly are evangelicals that believe the Bible is infallible. They popped into history a few hundred years back. Today, they are often called "Bible-Thumpers." Their religion is not properly called Christianity though. The Catholic and Orthodox Churches have been around for thousands of years, have legitimate historical claim going back to Christ through Apostles, and are essentially the communities that gave us the Scriptures we call "The Bible." According to them, the Bible is useful, powerful, divinely inspired, and worthy of all the blood, sweat, and tears it took for the Churches to pass it on. However, it isn't "infallible." It isn't God.

Perhaps the evangelical Bible thumbers' religion is better termed "idolatry" than "Christianity." For instance, to join the Evangelical Theological Society, one must confess that "the Bible alone, and the Bible in its entirety, is the Word of God written and is therefore inerrant in the [original manuscripts]." But think about that for a minute. The Christian scriptures say that the Christ, Jesus himself, is the Word of God. The same scriptures refer to the Spirit speaking to the minds of people as the Word of God. Jesus is still alive, and his Spirit still speaks. Therefore, the belief that "the Bible alone" is the Word of God is, at it's core, a rejection of the divinity of God's Son and Spirit.

The Christian Church never claimed the Bible is infallible. The Bible itself never calls itself infallible. Those who believe such nonsense are, in my opinion, either non-Christian as we speak or at the very least heading on a dangerous course toward a denial of Jesus' divinity when he comes again. The Pharisees and Sadducees, Bible-Thumpers of Jesus' day, worshiped Scripture similarly, and they ended up so screwed in the head that they tried to kill the very God they claimed to worship. I think people who say the Bible alone is to be trusted as "infallible" and "the Word of God" are often simply looking for a "god" they can use to judge others as less faithful or righteous than themselves. Limiting the Word of God to scripture allows them to. They are essentially modern incarnations of the very same self-righteous idolaters that Jesus vehemently opposed during his physical time here on Earth.