The FAA has the responsibility to verify via a paper trail as to how the work is going to be performed and signatures of approved field personnel stating that the work will be performed as documented, thus assuring responsibility is placed for work not being performed as approved.
It isn't their job to visually inspect the work although it is their option to do so.
I strongly disagree with that. The FAA hires qualified, experienced aircraft maintenance people as inspectors so that they can perform spot checks and inspect the inspectors.
Otherwise, all they need are high school graduates who can read.
The FAA inspectors don't have to inspect every aircraft, but they have to be able to observe and audit the airline maintenance workers to determine if they know what they are doing and whether they are qualified to perform the work.
Allow me to pose a question to you - would you want to fly an airline whose pilots were re-certified by an English major who followed a paper trail, or the airline whose pilots were re-certified by an FAA certified licensed pilot instructor who accompanied a randomly selected pilot on a "check ride"?