Earlier quoted context omitted.
As someone who recently worked in education... yes. Anecdotally, I tended to see it at the community-college level with students who owned a large-screen phone and didn't own a computer. I don't think anyone is writing whole research papers or serious lab reports on phones. A two-page reading response is totally doable. Something with footnotes or equations, not so much.
Yes, one can technically vomit out a few hundred words using a small touch screen. But the tools make it damn difficult to edit and re-organize text. Does this mean that all such reports are basically stream-of-consciousness writing instead of a more carefully polished piece of work?
The honest and unfortunate answer is, in my personal experience, that editing and re-organizing text doesn't often happen in students' papers regardless of the tools available to them. Not knowing how to type well is one thing, but a _lot_ of students get to college not knowing how to write a half-decent paper (and then still don't learn squat in their freshman composition class).