Is specifying a minimum word count beneficial for academic writing?

As we all know, during our higher education careers it is inevitable to be assigned essays or academic papers that require a minimum word-count.

I do not agree with your premise here. For my undergraduate and graduate students I rarely include a minimum word count. I do include a maximum word count (which students often want extended) for the reason you wrote: Encourage students to write concisely.

Minimum word counts do promote the things we want to avoid. Writing the same information with fewer words give greater power to the writing so encouraging students to do the opposite does not really do what I want to do.

That said, I do find that I have to be VERY clear with my students that writing too little can cause them to fail. I explain that when it comes to word count, there is a maximum, say 3,000 words, but no minimum. If they can show they understand everything they should understand in 500 words, great! However, unless they are an exceptional writer, they should expect to fail if they submit too little.

Well, you don't specify in which area you are. I certainly know that in mathematics and theoretical computer science, only a very weird professor would enforce a minimal length on a solution of a problem (which is a typical assignment: to solve a problem). You simply assign a problem and you think to yourself: "This should be for 2 or 3 pages of proof." To your surprise, the student writes a 10-line proof in a way in which you never treated the problem before (and maybe no one else either)!

So you never put a lower bound on the length of the solution, for the above reason. You can put a upper bound so that the student "can't simply list all possibilities", but even that is not necessary; however, it still of course makes sense if you have many students and a lack of time.

N.B.: One of my favourite scientific paper has 5 pages including abstract and references, and shortens a proof that was previously ~20 pages. Isn't that beautiful?

Let me start by saying I'm an undergraduate, so take me as seriously as you feel I deserve. I've TA'd for a 200-level class with a fair amount of writing, which meant grading lots of papers, and dealing with students who need to have a word/length requirement to be happy. I also have worked in journalism both as a writer and editor (again, college paper), so I've done lots of writing, and spent a lot of time working with writers on their articles.

In class, length is seen as a good thing, while in journalism, it's seen almost as a bad thing (due to space requirements). Dealing with tight space constraints was very tough for me at first, but after doing it for a few years I've learned to write compact stuff. You write better when every word is a gift. You really think about what you can cover in a given space, and how to give every word as much impact as possible. You think about structure more, knowing you won't have room re-summarize later, and you don't bring up anything that's not essential to what you're writing. It's harder, but it makes you better.

Giving long length requirements seemed to have the opposite effect. Topics diverge, and structure can easily be ignored. Writing/syntax is encouraged to be verbose. I see many writers come onto staff used to writing they do in class, and what I've noticed is that their writing often lacks clarity and purpose.

Most of what I do as an editor/teacher is ask questions like, "What exactly are you trying to say?" and "Explain this to me like I'm a 5-year-old." I find that this really helps, and that good writing follows good and clear ideas. This is regardless of the length of assignment, but I think having limited space forces students to do this.