This post has been closed as a duplicate. All votes have been moved to the original: Give PMs ability to prevent users from Logging Time to Completed Tasks
If you close a task, and want to prevent anyone from logging time on it after that point, you have to go into Sharing Settings and remove people's contribute access to log hours. It would be much faster, and more intuitive, if closing/completing the task automatically removed everyone's ability to log time on it.