Moreover, why not put a separate tab on the control center overlay that would display current permissions for running app as well as number of requests made that used that permission. If you drill in particular permission it could display history of requests for that particular API.
Having something like this would also allow for better audits. A separate app could show requests against a particular API by all apps as well as allow filtering. Other useful stats would be average number of requests per day per API per app and a graph of API calls by time of day. If nothing else this would allow to quickly identify rogue applications that make too many requests and drain battery.
On the topic of battery drain, I think that "allow to run in background" and "run as a service" would be a useful permissions as well. First one you would want to give to music players and to GPS applications, for additional control include time app allowed to run in the background before it is killed. Second permission would cover apps like IM and Facebook that are known to be tremendous battery hogs.