Grand Canyon overflight proposal

As a guy who has hiked out of the canyon with a 65 year old with pace
maker (11 hours), I personally know it can be done. On the other hand
a chance to see this wonder of the world from the sky would add a whole
new dimension to the Grand Canyon experience. I don't understand why
the park system can't offer a limited number of permits only to be used
on say a thursday or tuesday, or a day that is commonly a slow and low
attendance day. This way planes don't fly everyday and trips, up or
down can be scheduled to avoid the problem.
Lou