I'm going to play devil's advocate here. It's stated that taking points off the grade for a late assignment "replicates the deadline criterion of the work world". No, it doesn't. In my field, if you are late, you lose the client, you lose money and, ultimately, you will lose your job. Do this enough, you lose your business. There are no valid "Oh, we didn't get finished on time...." excuses because client deadlines are written in stone.
Added Note: I give each student a sheet outlining the project and the due date and time. I also put this info online… >>>