Should you tell grad students to apply for grants you know they won't get? I am a humanities professor at a middling university in the United States.  My department has a poorly funded Ph.D. program, which attracts second-tier students at best. (The good Ph.D. students go to programs that can afford to fund them fully, it seems.)

Each year, I typically have my Ph.D. students apply to all of the relevant major grants (Fulbright, Mellon stuff, etc.) that would fund their dissertation research.  None has ever gotten a grant, nor have I ever had a student who I thought had a remote chance of getting one. Their essays are usually poorly written, despite lots of editing help from me. (By poorly written, I mean there are really fundamental writing issues, like incomplete sentences. I point these out to them to the extent possible but I can't write their essays for them, and I don't catch every error they make.) Frankly, I think our Ph.D. students are just not of the caliber that are going to win grant contests where only the top 1 or 2 percent of applicants are funded.

I am wondering if I should continue to have the students apply to these grants each year. On one hand, it feels like a waste of their time (not to mention mine, and the application reviewers') to have them write grant essays for fellowships that they basically have no chance of getting. On the other hand, I can't know for certain that they will never get grants -- strange things happen -- and more importantly, I think that writing the application essays is good for forcing them to think through their dissertation projects. But maybe that time would be better spent doing research so they can finish our program without accumulating massive amounts of debt (because we have poor funding, many of them borrow money to attend -- for which reason I think we should not even admit students if we can't fund them, but that is a separate issue).

For the record, I do strongly encourage my students to apply for smaller-ticket grants -- the kind that pay $500 or $1000 to support a certain type of project, or go to a specific research site, etc. These grants are usually more obscure, more specialized and less competitive, and the students have a better record of getting them. (I also work very hard with them on these smaller grant applications because I know their chances are better.) But when it comes to the big-name, Fulbright-esque grants, the prospects just seem hopelessly dim, and I wonder if the time everyone spends on their applications is worth it.
If what you say about your students' writing skills and their chances of getting a major grant is accurate, I would say that it's a complete waste of everyone's time - theirs, yours, and the reviewers - to have them write such major grant proposals. Forget about using such proposal writing as a vehicle to improve their writing skills. The experience won't benefit them if their current writing skills are really as bad as you say they are. Instead, have them focus on the smaller-ticket grants. If any of them show evidence of more promise and growth after such experiences, then you can direct these more promising students towards targets that are higher up on the grant ladder.