I'm in k-12 education (I specifically work with 7-12, but this issue applies more generally within k-12), and our major driver of custom due dates would be students on an IEP or 504, which are both parts of US education law that lead to some students with disabilities having custom education plans that given them certain accommodations in their courses.
A common accommodation within such plans is for a student to be allowed to turn n work "x" days late. For example, Stu Dent might be on an IEP that states that he can turn in all work up to one week late, or Ex Ample might have it written into her plan that she can turn in all assignments through the last day in the term. Right now, I would rely on Stu Dent's case manager to email me so I can manually give him a new due date each time he needs one, or for Ex Ample to send me a message letting me know which assignments she needs re-opened. (Theoretically, I might go in and add this exception by hand to all assignments in the course for all such students, but that does not scale well, so in practice we tend to do upon request instead of by default, which would be preferable.)
So, settings we might use would be things like "change all of Stu Dent's 'open until' dates to be exactly two weeks later than the 'everybody else' open until date" or "change all of Ex Ample's 'open until' dates to be Specific Date".
Another common use case for us would be students who enroll a week or two late. It would be be nice to have the option to either "compress" all due dates and 'open until' dates within a specified range for a late start student (for example, for a student who started the second week of the term to have the work from weeks 1, 2, 3, and 4 re-distributed to be due in weeks 2, 3, and 4 so they'd have 3 weeks to get 4 weeks of work done and be caught up). It would also be useful,and much simpler to implement, to be able to simply set all of their "open until" dates for assignments within the first x days or weeks to a specific later date to give them that catch-up time without the structure of custom due dates.
This is our first year using Canvas, and I have not yet had time to look at the API and existing tools to determine which automated tools we should be using, so right now we're doing all of this by hand through the web interface. I was planning to research automation/batch processing tools over the summer after I better understand the workflow of using Canvas and how settings interrelate with each other. (For example, I just got bit by the fact that the multiple grading periods feature needs all assignments to have due dates, not just close dates, in order to function. I'd prefer to learn as many of those quirks as possible before spending time on automation so the automated solution does not create such issues.)