Comment by jurjenh

I think that it serves to make reading an essay more fluid, as you can crop a lot of unnecessary information this way. If every "it turns out" was to follow the path that came to the conclusion, then there'd be a lot of extra detail that would divert the reader from the intended direction, without providing necessary information.

And if the exact path is illuminating in some way, but distracting from the original intent, then it would serve to put the explanation in a footnote.