If you have just finished a challenging pose, take headstand for example, adopting childs pose straight after may not be the wisest thing for your body and for recovery. Just because this is the norm in yoga circles and yoga websites, doesn't mean it should be a standard practice. When we view recovery from an exercise point of view, childs pose is not the best option.
After headstand, if you wish to fully recover, you need oxygen. Oxygen works to alleviate peripheral fatigue because oxygen can help your cells remove acid. Simply put, steady breathing begins to replenish the oxygen in your body, which helps to refill the myoglobin oxygen stores in your muscles. Making you ready for the next pose.