That’s not any different. Now how late are you allowed to submit? 5 PM? Sometime at night? Midnight? How many people are allowed to submit late? What if word gets out that everybody is allowed to? You get the exact same problem, except that more of the professor and TA’s time is wasted, and the whole process now has favoritism baked in.

I have seen deadlines wrap all the way around a 24 hour cycle in this way. 5 PM is bad because people want to work at night, so delay to midnight. Well, people aren’t finishing, so delay to 5 AM, since everybody would be asleep then. Well now people are blaming you for “forcing” them to do all nighters, so delay to 9 AM. Now people say that’s unreasonable, because submitting later in the workday wouldn’t hurt anyone. So delay to 5 PM.