I agree, I am the Customer Success Lead for a SaaS company and this would make managing and delegating much more efficient. It would be a huge value if there was a check-box where I can state whether I would like a confirmation notification when the task is complete or not. My account managers are supposed to tell me when certain tasks are complete, I could do a better job at coaching them with this feature.
It would also be great to know who assigned the task.