Most people are the opposite and prefer to wait until the last minute. Ultimately it takes us both the same amount of time (one minute), but my minute arrives early but their minute comes later. You might say there's no difference, but for work that requires editing and detail, it's important to have more time available if needed. Writing a paper isn't like dusting the furniture; odds are you'll need to change things after the fact.
The biggest thing I struggle with when getting my students to work isn't getting them to turn in work (they do), nor getting them to write quality pieces of work (most of them can rise to the occasion), but getting them to use the time. I try to give students enough time to (theoretically) complete all work in class, but most of the time it's wasted. They'll pretend to work, perhaps fooling me, and maybe even fooling themselves, but in the end, they're not using the time. They're rushing...and planning to wait until the last minute. It's a difficult task teaching someone to slow down and take more time than they feel they need...but really, that will ultimately make all the difference.