For online learning the grades aren't likely to matter, people are mainly doing it to get the knowledge. I can see though if you distilled it down into telling people what you got, say a B, won't reflect how well you actually learned the content if the B was only the result of late handins.
On the other side of the coin though people are relying on the strictness of handin times in order to motivate them to get through the course in a reasonable amount of time.
Timed based on a final date to finish everything is a compromise but wouldn't work for everyone, as some would loose motivation after falling too far behind. So maybe there needs to be a few deadlines throughout the course, but not a weekly one.
The only course I have done I ended up missing a week handin as well, I think most working people would be in the same boat.