Assuming the 98% applies to both false negatives and positives:
For a given 20k person school, assuming they each write only one paper a year that's run through this, an administrator gets to expel 400 students a year!
What fun!
The more insidious issues is you have a sub-population of students that write in the "wrong" way. That means the average student might never get a strike, but this unlucky sub-population might get multiple strikes. That would seem to point to the results being "correct" -- after all, you'd expect a cheater to cheat multiple times.
If this population skew is significant enough -- say, 1% of the population writes in the "wrong" way, and the multiplier effect is 10x as strong for them -- you might never get a flag for a normal student. But what you're measuring is not cheating, but deviation from the norm in writing style.
Memory that pops up is Barton Fink being told to write a script for a wrestling film.
Also sort of topical in high school had a quiz on a short story that I had not read. But I had read some of the authors other short stories. So I started out with 'While I failed to read 'story title'. Based on the author and the title I think the story is about bla bla. And the teacher took off 2 pts for not reading the story first.