Long story short is that without deadlines people tend to push off work to the latest possible moment, at which point they tend not to be able to do as much as they thought they could in that short time space, so it actually causes more stresses on them than it would have to have had a series of deadlines along the way.
Edit: Here's some more research which backs up why your conclusion may not be correct: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3374478/ Granted it is probably too early in the research of this area to say your conclusions are wrong, just that the research is leaning that way
Professionally, I've learned my lesson and while I've had some moments of procrastination (especially for tasks that I have little to no motivation for), I tend to work more steadily than I did in those first few years of college and I rarely run up against a deadline (soft or hard).
However, I've worked with plenty of software developers who wait until the last perceived moment and work crazy hours to try to meet the deadline. I'm not sure what they would do if they didn't have that deadline. I suppose they would either get fired for lack of productivity or just be productive enough when nudged to keep their jobs.
Well, with only five minutes left they are! Especially if it means they will lose the game if they don't.
I agree with your premise to just keep pushing forward, always making progress — but some things do have deadlines which are unavoidable.