"Don't know why, but it works."
The diameter of the string post increases as it gets closer to the headstock. Thus, the string bends around the post at a greater angle, reducing the stress concentration. Consider the proverbial example of bending a paperclip back and forth. If bent at a sharp angle, like in the jaws of pliers, it will break rather quickly. Now hold a paper clip between your round fingers, it will take many more cycles to break the clip.
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