I tried to think of the question from both sides, taking into account not only my expectations as a writer sitting down at the keyboard, but as a reader when picking up the work of another. And I think my answer can be summed up in one simple phrase. What do we owe our readers? "A good story."
That deserves a little unpacking. A good story, I think, is one that has an ending. And so writers owe their readers an ending. If you begin a story that can't be comfortably fit into one volume, fair enough, but writers should ask their readers to begin reading a story if they aren't ever going to provide the ending. Obviously, there are real-world complications that can get in the way, and some writers have the poor foresight to die before finishing their tales, but all things being equal I think that writers should finish what they start.
What else does "a good story" mean? Well, I think that varies a bit from reader to reader, but in general it means that there should be some point to what's going on, that stuff should go on, that there should be characters (hopefully interesting ones) in a setting doing stuff (or at least talking ab0ut doing stuff, or maybe just thinking about doing stuff). There should be some entertaining element to the story, on some level, and if the writer can manage to squeeze a little enlightenment in there, so much the better.
This "entertainment" and/or "enlightenment" business is something I've thought about a lot over the years, and which I may talk about again at some point. To cut to the chase, though, I've come to look at myself as an entertainer, primarily. Not every writer is the same, obviously, and there are those who put more value on enlightening their audience--teaching them something, or portraying some truth, however painful or difficult to hear--but as for me, I'm Sammy Davis, Jr. I'm a song-and-dance-man, and while I harbor ambitions of working in a bit of Truth in my fiction whenever possible, I know that if I have to choose only one or the other, I'm going with entertainment.
But my thoughts on the entertainment/enlightenment question aside, the fact is that I think that readers deserve a story that exists for a reason. That reason may be to entertain them for a short while, to thrill or amuse them. That reason may be to bring home some underlying truth about the human condition, or a glimpse into the lives of others that we wouldn't otherwise have gotten. But whether the story is pure entertainment or some kind of enlightenment tract, the important thing is that the story has to be for something. If a piece of writing neither entertains nor enlightens, then it might be stylistically accomplished, it might have all sorts of pretty bells and whistles, it might be a dandy-fine writing exercise, but it isn't a story. And readers are owed more than that.