I relate to this issue. I teach at Western Ontario, and I am uncomfortable with the standard practice of granting extensions because of illness for the same reasons outlined by the author. Two years ago, I tried to combat this problem by telling the class that everyone would be given a one-week extension for any assignments without the need of any kind of documentation. I thought that this would help students manage their time and relieve the schedules of doctors and the students themselves. Unfortunately, all but a small number of students simply treated the one-week extension as the new due date and the same problems appeared, only a week later. My idea needs work, but I would like to see how effective it could be if a critical mass of classes adopted the same policy: students might learn to set their own deadlines if they had that ability in all of their classes.

Dealing with makeup tests is another story.