I'd like to do this, instead of checking off tasks, for tasks that can't be completed for one reason or another. I don't want to completely delete the task, because that loses information.
For similar reasons, I don't want to "cheat" and check off a task that was not successfully completed in real life.
Ideally, this "Discard" option, would retire a task from the importance list, similarly to checking it off, but without actually checking it off. A filter option "Show Discarded Tasks" would work similarly to the existing Show Completed Tasks.
You could change its Status to Cancelled. That would keep it hidden if the Hide Deferred Tasks filter is on. You could also give it a -1 Priority if you use that filter. That would allow you to keep Cancelled tasks hidden, but see other types of Deferred tasks.