Abstract (I hate "tl;dr"): By using a graduated late penalty function with second-granularity, you achieve several desiderata:

(1) Ensure submission within a week of a nominal deadline. (2) Be perfectly even-handed without being draconian. (3) Eliminate whining and excuses.

Most importantly, it's socially efficient, incentivizing students to take exactly as much extra time as they need (to a point).