Critical Chain changes the way tasks are managed. Daily status helps to keep people’s attention on one task. Asking the person for remaining duration has them thinking about what they still have to do. It also becomes a subtle commitment for them.
Project status is current and reasonably accurate. Buffer Management identifies the tasks that are most impacting the project due date. The most important tasks get priority and focus to get them done. Problems show up quickly so they can be dealt with. Projects get done fast and the people doing them like it.