The objections all of the contributors are on target and these are true with all KPIs. You establish a metric to increased desired behavior, that desired behavior is "paid for" by the removal of other behaviors, some of which are also desired. This is why establishing your KPIs is very challenging and you need to do so with care.
A balanced approach is called for here, where if you are measuring the reduction of defects in quality, you need to also measure, and reward, those other behaviors that will likely be affected, too. For example, if I am being measured on quality, I am going to slow down and double check my work. So you have to counter that with a measurement on time. I'd also take less risks, which in many environments you do not want. So you have to counter that. You have to also be careful with cause and effect, the relationship between the independent variable (what you manipulate) and the dependent variable (the result). What seems intuitive, logical, and even "common sense" is too many times not true. You would think increasing someone's wage would have positive effects on morale and work effort. In fact, morale is not touched, or it actually drops, and work effort will eventually decrease as the labor supply curve suggests.
It might be that scoring defects is not the solution to increasing quality but rather scoring those behaviors that lead to quality, i.e., leading indicators. We know increased skill should mean higher performance, so perhaps there is a KPI or two that will motivate skill acquisition and mastery.