I don't offer extra credit unless there is some reason why I'm willing to offer this to all of the students in my course (which I've done once in a blue moon when I had a really good reason. Otherwise, I don't do it. I don't think there's a way to justify that it's fair and equitable to all members of the class to offer extra credit to some students and not all of them. Moreover, I think it creates unrealistic expectations for both college and life. Students ask for this because many of them have been taught by their high school teachers (who have been told to do so by admin) that you can skip the work you don't want to do and then ask for extra credit later. That's not how any of this works in college or in life. It strikes me as setting them up for failure in a lot of ways and teaches them that they can skip the hard things (like actually mastering the course material) for a quick fix later.

Before the "but what if they are struggling with something" people come out of the woodwork (and they will), I am very open to an occasional extension for a student who communicates before a deadline if something comes up or life happens. What I am not open to is bailing a student out after they haven't done that and turn in work that doesn't reflect actual mastery (which is why we grade them to begin with... it's not just for funsies) or don't turn in anything at all. Two very different things.