@e0 if it's a task/program IN the task manager then no. You don't need special permissions. I cant' speak for all teams, or everyone but I believe anyone can open the task manager and end a task.
However, any and all of the "vital" programs on your computer will not be able to be "shut down" via "end task" in the task manager. Essentially, if you click the little arrow on the bottom right side of your desktop by the clock, most of those programs are never gonna be shut down via task manager. They will infinitely restart/reload and are always going to be active...
Now, this is strictly speaking of ending a task via task manager - the conventional way! There is absolutely 100% ways to stop these tasks from running and/or starting up after shutting it down but, it's more involved and has to do with the registry, among other major items. I wouldn't recommend doing tbh...
Back in the day of my ProSupport career, there was a program called "ICE" which essentially was used for managers to monitor your calls and/or listen in on calls. For whatever reason, that was a program you could simply just exit out of via task manager lol. Which I did often enough.