The park service allows automobiles, needlessly loud motorcycles, generators for RVs (within limits), and any number of greater nuisances. (Including the other 20,000 people who came the the Grand Canyon south rim on the day I did.)
And they restrict where all those things can go, too. If they restricted drones the same way, they might as well ban them outright.
Plenty of other things interrupt views, like tripods or even other human standing nearby. A general ban on deliberate or extreme interruption is reasonable, but a total ban on remote controlled aircraft is not.
The problem with things in the sky is that they visible (and often audible) from long distances. A single noisy drone might affect several square miles, covering hundreds or thousands of people (depending on the location). A guy hiding behind a tree with a tripod will likely affect a few square yards, and a tiny handful of people.
Look, you're right. Used tactfully, by reasonable people, they would absolutely make a fantastic photography platform, and probably not be too intrusive.
However, I have insight to the daily lives of park wardens in popular national parks.
There aren't many of them, they have to cover huge areas, and they spend their days stopping people lighting things on fire, breaking things and taking them away, writing their names on things and trying to put their kids on the backs of the wildlife for photos (I kid you not, it happens once or twice every summer).
I guarantee that if drones were permitted, some people would be buzzing them around the wildlife from a safe distance. This kind of added stress on the animals can and does lead to failure to breed, which has very bad effects on the viability of species, particularly for the less populous apex predators (bears, wolves, big cats).
From the parks point of view, they have to come with policy based on gross population behaviour. They can't supervise or train everyone using the park, so they have to come up with simple policies that can be blanket applied. Unfortunately, the potential for abuse with drones is probably pretty high, thus the ban.
How frustrating would it be if you couldn't get that nice photo without someone elses drone in it from your flying drone?
I live near the Banff National Park in Canada, and it's a continuous game of tug-of-war for the wardens trying to decide what activities to allow in the park. With no restrictions, the place would quickly be overrun. When the point is to experience the wilderness, you have to be very aware that some activities can very quickly, and with very few people, destroy that experience for everyone.