I think it is interesting how teachers tend to teach to the kind of student they are. I am a timely student. One thing I really appreciate is timely feedback. I took a course once where we often didn't get our homework assignments back for several weeks. By the time you got the corrections, the feedback was basically meaningless. When I have taught, I have always tried to give feedback by the next class period. I also find this helpful in steering what to focus on during class time. If many people missed a particular question, then it deserves more attention during class. For these reasons, I have usually had weekly assignments, so that students are required to practice their new-found knowledge shortly after learning it, and then get feedback quickly. This will of course vary from subject to subject. I have also experimented with having different days of the week for deadlines. I tried Fridays, and students complained that they were too busy during the week. I tried Mondays, and I got a bunch of last-minute e-mails on Sunday, and I usually don't work on the weekends. So I decided Tuesday or Wednesday is best. This gives the students time to work on the weekend if they want to, and time for me to answer their questions the day before the assignment is due.
Besides procrastination, is there any reason why having deadlines later would be beneficial for students or the teacher? It seems that you can almost make a universal law that shorter feedback cycles make for better course correction in almost any type of system.
I agree that the classes I've taken where there has been significantly shorter feedback cycles I've always felt more engaged.
Whenever I hear about instructors complaining about student procrastination, it makes me think back to when I implemented/managed a system for academics to make a certain type of submission.. and over half of the submissions were always after the deadline during the "last second extension". Physicians, heal thyself :)
The most effective manner I ever used was some variation on the "due on or before but not after" deadline. This could be used with extra points (reward) if turned in anytime in the "before" range and no reward (but acceptance) if turned in "on".