We implemented a coaching system for our support team about a year ago with the explicit purpose that individual coaching does not directly affect KPI, and that as much coaching can and should be done freely without worry of impacting the support team. The system tracks both the person being coached and their team lead who does the coaching. The coaching is directed to be as instructive as possible, that it's not about punishment, but better ways of handling specific technical situations or adherence to the support policy.
Long term reviews consider not just the person being coached, but also the leader as well, as a high number of coaching options across multiple persons on the same team would suggest an issue with the leadership as the root cause, and more qualitative reviews focus on that element as well. The entire point is to ensure that Performance Improvement Plans don't have to be a thing, and that there is constructive feedback flowing into the system.
Adoption was slow, but with strict adherence to what a coaching instruction must include, we've seen exceptionally high improvement and much calmer conversations when mistakes are made since the support persons realize "this isn't a KPI penalty or a PIP; it's just trying to prevent that." Having the system "open", i.e., the support persons can see every entry they have at any time with a few clicks of a button means no secrets.
It's a lot of documenting, but so far we're seeing a ton of success with it and positive feedback to having this process for constructive criticism, and the focus on also considering "this might be a leadership issue" also helps add some comfort.