I think this is a really interesting subject -- the progression of tech allowed/encouraged/required in education. My kids use calculators to do parts of their math assignments in junior high and highschool, with the teachers' logic that what they want the kids doing is the algebra and trigonometry, and don't want them wasting time on addition, subtraction, multiplication, and division of large numbers, or looking up sin, cos, and tan values in a table (like I had to do in highschool math). Calculator use was rigidly prohibited in my schools, until college, where we were required to use graphing calculators for my math classes (math, physics, and econ major). My parents were required to learn how to use slide rules!
I don't care much for the grammar checkers, but I sure rely on spell checkers. I'm a reasonable (certainly not great) speller, but typos produce a lot of spelling errors that are easy to miss without computer help.
I think for researching information, ANY source or method is good, PROVIDED (important) that the student learns how to check the validity of the source. Even in printed science publications, there are good journals that involve heavy peer review and others that will take just about anything without much vetting. A good article found via Google or Bing on the website of a reputable site, say, a Johns Hopkins page summarizing some medical or astronomical principle, may well be better than something found in a library in a lesser journal.
All of that said, I'll admit that AI seems different if it's actually creating the paper for you, because then the student may know literally nothing about the subject matter or the writing process. I also think that writing on a subject CREATES AND SOLIDIFIES knowledge. We learn as we write. Explaining a subject requires your knowledge to connect all the points from start to finish, often revealing gaps in what we think we know. This is why teaching a subject also forces us to learn it better.
So if I were God Emperor of academics, I would permit using AI for research, but still require a bibliography with original source references (so the AI is just to get a high level understanding, but sources must still be cited to defend any specific points the student raises), but prohibit using AI to create anything, unless it were a class on using AI for that purpose.