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I'm not sure it completely has abandoned allegorical interpretation. The PCA church still takes much of Revelation to be allegorical, although the rest of the United States doesn't so much anymore... a result of John Nelson Darby and Cyrus Scofield in the 19th century, who came out with the Scofield Study Bible, with Darby's dispensational, and somewhat more literal interpretation of Revelation.
Many of Jesus parables are still taken allegorically, though they're often coupled with a philosophical Occam's Razor in order to come up with the simplest explanation.
I don't think it's that we don't take parts of the Bible allegorically, I think it's just that we no longer go out of our way to do so, unless the text seems to call for it.
That being said, much of the shift that you're referring to, at least according to Wikipedia, comes from Luther and Calvin, the former of whom came up with the principle of scriptura sui ipsius interpres (Scripture is it's own interpreter), and the latter of whom came with the principle: brevitas et facilitas, brief and relevant. That, combined with the rationalist and humanist movements of the 15th and 16th centuries combined to make the shift.