Use of words like "herein" in research articles
Here's a factual and quantifiable answer to your question :)



As you can see in the Google NGram, the word "herein" has been the popular way to convey this idea historically but has since 1920 lost popularity. "in this study" and "in this paper" together outweigh "herein" almost double up at this point.

(end:facts, begin: speculation)
Take the following with a pinch of salt; but if you consider why this is the case, I'd say "herein" is the old way of saying the exact same thing as the other two. Sometimes people associate older phrasing with being finer, more eloquent and indeed sometimes even more intellectual, in a Twain-esque way. Please note that I am not accusing your colleague of thinking in this way, but sometimes people tend to choose the fancier/older word because it "sounds better". 

I have to say I really don't buy the argument of "herein" being shorter; you save 2 words or 6 characters (incl. whitespace). I would presume that you don't refer to the article more than 4-5 times throughout the course of the paper, so your saving is approximately 10 words, or 30 characters, which is not that much. I am willing to accept that excuse for an abstract maybe but certainly not for a research article where you typically have 5000 words or more to describe your work.