The next time you assign an essay, don't make any requirements about what students are able to use in the process of writing: Word grammar-check, spell-check, grammar software, whatever they want. Watch what they do. Watch carefully the process and what happens between when they think of something to say, and when they actually have something on paper. The computer is involved every step of the way, and you should be aware of how that influences the process.
Now of course, you could tell them NO. Don't use it, I don't want to see you using it, it's wrong (you could even disable the computers that they are using). What that means is, they would use it all the time, except when they are in your class. But then you might as well be teaching primitive hieroglyphics, because it would be just as useful - it would be primitive writing compared to what they would use every day. They would produce things that would look nothing like what they would normally produce. You would have a much clearer view of what they actually know. It also might be easier for you to figure out what they meant, since the computer would no longer alter what they write making it harder for you to interpret. So, sure, there would be advantages. But the biggest disadvantage is that you would be teaching them to write without using any of the tools they would normally use. It would be like teaching someone to drive a car, only using a Model T. One side of us says "that's the real driving, that's what driving was meant to be." But the other side says, "You were unable to teach the things they need the most," i.e. how to use the tools of the modern car.
Intuitively, there is something gratifying about teaching to drive on a Model T. That's the real thing, right? All the modern conveniences just get in the way, don't they? If you taught someone the true skill, unadorned, unchanged, wouldn't that be better?
No, they wouldn't let you, because it would be unsafe to put someone in a new car without the awareness of what the modern tools do. And the same with writing in the modern world. In the old days, it was harder to manage a clutch, make a turn, etc. so you spent more time mastering that stuff. In the modern world, if you spent a week learning how to use a clutch, you'd be wasting your time. You should teach them how to write as we know the process today.
That's why you should recognize the machine and its role. Tell them the difference between one grammar check and the other. Teach them how to use spell-check and avoid errors. Get them to use their memory for the stuff they need to memorize.
In the future, this might not include words. Why should they learn new words, when the machine can just provide them? Ah, but what the machine can't do, is construct them into simple, meaningful sentences. Only you can teach them that!