Even the most careful, thoughtful, and professional person will screw up at their job sometimes. It's only if the same screwup is made twice that jobs should be on the line.

The first time is a learning experience, the second time is a demonstration of incompetence.

If you can all your competent people the first time they make a mistake, suddenly you won't have competent people anymore in your misguided quest for perfection.

Their peers will learn that 'screw ups' on whatever arbitrary scale, which are as common as human, will be punished by loss of employment, plus all of the negatives that status carries. This will teach them to become militantly risk averse and, by proxy, utterly afraid of and resistant to change. Meanwhile, the folks you let go, the ones who truly learned the lesson, end up using their newfound experience to improve processes elsewhere.