NZFlyingKiwi is right on why DOC have the rule, but also as Ngai Tahu have ownership of Aoraki/Mount Cook, they do request that climbers do not stand on the summit, nor aircraft fly in close proximity of the summit as it considered Tapu.
But as a climber, the last thing I want is to climb to the summit of Mount Cook and then have a helicopter try and blow me off the top as it whizzes by. For those who haven't been to the summit, the summit ridge is usually a wind blown ridge about two feet across, which a drop about 6000' down.