Ability to set the repetition (eg every 5 days after completion), but then the task just sits there (& rolls over to the next day if not done), until it’s marked complete, when the next copy is generated (in this example, for 5 days ahead).

Plenty of task managers (Todoist, Things etc) have this. It’s really helpful for tasks that should be done regularly but don’t necessarily have a fixed schedule. It would also solve the problem of multiple copies of a daily task building up - you could set to repeat “one day after completion” so it would only create the next occurrence once you did the previous one.