Alright, playing with sticklebricks done, what have I learned?
The answer shouldn't have surprised me. If you find someone utterly incapable of doing their job, take them out and, presuming you can't sack them, make them responsible for quality control. In improving the quality by removing the main cause of error, you reduce their new role to one of trying to look busy and justifying their existence, none of which does any positive harm to the product. Eventually (hopefully) someone will discover that they serve no useful purpose, merely to depress the profit margin, and let them go.
I'm not sure that this was the intended lesson though.
In addition, I learned the trainers have no sense of irony, local management need a refresher in basic ethics, and that an autonomous collective with a grasp of the public service ethos is better equipped to deliver than the structure I currently operate within.
I don't think that I was suppose to learn that either...
Finally, I was reminded that there is greater joy and personal satisfaction in seeing a task through from beginning to end, taking personal responsibility for your own successes and failures and delivering what your customer needs than in being a anonymous, soulless operative standing next to a conveyor belt.
And boy, I definitely wasn't supposed to learn that...