Power
You know that scene in Star Wars where The Emperor shows up to inspect the Death Star, and all of the stormtroopers are lined up in rows, shaking in their little white plastic pants as he walks by? That's what it's like for a lot of aviation safety inspectors when they walk into an airport hanger full of mechanics.
The mechanics are worried, and for good reason; if the inspector finds something wrong, there's no way for her to make "if you do this again, people could die" sound warm and fuzzy.
Is that power? If it is, it's probably not the sort most ASIs signed up for. The real, lasting power of a certified inspector is in the collective influence they exert over the safety of every single passenger that flies out of a U.S. airport. While the internet links the world digitally, planes link the world physically, making each inspector responsible for guarding a small percentage of that global connection. Pretty cool, huh?
Just don't screw it up.