Winners sometimes quit, quitters sometimes win
Oddly enough, in the two weeks since I gave notice, the immediate managers showed no curiosity at all about why I was leaving. Surely such information would be useful? On the other hand, the person from HR who conducted my exit interview yesterday (who looked exactly like Taylor Swift, I swear to Satan) asked plenty about it and took a lot of notes, so maybe the company will learn something after all.
I did report my concerns about all the coughing around the workplace to one of the managers and she said they'll look into it. What the outcome of that will be, I guess I'll never know.