This is coming from a little bit of a different point of view, so bear with me!
I will be a junior in college next year. I *just* finished my semester yesterday. Typically I am VERY busy with all my classes. I am a biology/pre-med major and if I'm not in class, I am doing homework, or working at my job to make the extra money I have to spend on essential things like groceries and cleaning supplies for my apartment.
Honestly, if a professor of mine did not show up for a scheduled exam, I would probably be pretty upset. I have to plan my week very carefully so that my classes and my labwork/classwork do not over lap. I am very understanding that situations do come up, but if a professor expected me to take a "take home" final within 24 hours, I would probably have a difficult time doing so. Then again, this is coming from a student who takes fairly difficult classes in which take home tests are no easy task! For me, 24 hours is not a very long time to complete an entire test, especially after I had already planned to take the test at the scheduled time.
I did have one professor who showed up late to a final last week. She was almost 20 minutes late. When she got to class, she said she was late because the copy machine was not working properly. I have to say I was pretty upset that I had to wait 20 minutes because a professor waited until the last minute to copy her tests! (I'm not saying that it was your fault you were not able to make the class at all...just offering a story so you can understand where I am coming from.)
Granted, I probably would have emailed you ahead of time to state that I would have scheduling conflicts, but I would still be somewhat upset about the extra work I would have to do at the end of an already crazy semester! Things happen and we can't always control them. I would definitely be more understanding in this situation if my professor emailed me with an apology and explained the situation. I realize some students are just plain lazy, but not all of us are! As I said before, 24 hours is not that long for us busy college students (Even if there are only a few of us!).
Hopefully you won't have to fail too many students over this. I know most of my finals don't really count for all that much, so a low grade on the final doesn't really affect the overall grade providing the student did well enough on the previous tests.