If you are working on a schedule, you want to ensure that the people you delegate the tasks to can get the job done right and on time. So you delegate them to people you trust.
Without trust, delegation becomes a source of frustration and disappointment. You may even end up micromanaging the delegated task because you need to figure out if it gets completed.
But when tasks are delegated to the right people who take ownership of whatever is assigned to them gives you peace of mind.