In my real life, I'm a faculty member in Computer Science with a focus on first-year learning. While some might argue otherwise, I'm very interested in my student's success. Success in first-year has something to do with learning content, but a large component has to do with understanding that they are in charge of their learning, and that they need a strategy for how they are going to go about it. I find that if they get the second part right (thinking about and planning how they are going to learn), then the first part becomes relatively easy.
So here's an argument for finishing early. I have no empirical models - just a ton of observations. The red line represents stress as a deadline approaches, with the submission not complete. Notice that at the last moment it's due the stress is off-the-chart high. Now look at common sense (blue line), again assuming the submission is not complete. Notice that at the last moment the submission is due there is no common sense left. So the message is that the closer to the deadline, the more likely you are to want to make a bad (stress-induced) choice, and the less oversight (common sense) you have to resist the bad idea. This can't be a good mix, can it?
Take a moment to think about a deadline. It does not represent the time that something must be handed in. Nope, instead it represents the last possible time that something can be handed in. The message? Complete the deliverable in advance, before the stress gets stupid and so do you. You do better work for less stress and more peace. Isn't that where you want to work?
For you teachers out there, what are some of the silly things that your students have done when they work outside of the envelope?