The uncertainty already inherent to the existing process is high enough in my opinion, either the software or the hand counter would equally meet the real objec

The uncertainty already inherent to the existing process is high enough in my opinion, either the software or the hand counter would equally meet the real objective here: providing a point to audit for reportable metrics. While a dungeon master presiding over a hopeful throw for critical hits would be a solution, I don't think the TSA wants to make security theater entertaining - it makes the accidental nature of the whole endeavor obvious.