This doesn't work when users may need to run arbitrary (or user-defined) containers. You can only sudo so much... But, perhaps you could restrict it to "sudo docker run". I'll have to give that a try. But that would make it extraordinarily more difficult for a user to stop / rm / kill a container. Plus, it's not like docker has the concept of an "owner" for a container - does it?
Nonetheless, you shouldn't need to run anything as root in order to start a container that doesn't require extra privileges .