The kind of automatic splitting of a task across multiple days is probably doable, but not in the way that you describe. Setting it up and maintaining it would be a pain, largely because of what you’d need to do to your task records to pull it off.
Remember that each entry on a calendar view represents a single record. To have a task appear to be split across multiple dates, you’d need two records for the task: one for the portion that’s on the first day, the other for the remainder on the next day. This kind of split could be set up with the help of a script, and with a robust-enough setup you might be able to interactively drag the record around on the calendar and have the split auto-update (though not in real time). That said, my gut says that such a setup would be more annoying to use than actually helpful.