I agree. I work in a matrixed consulting organization. I have a "People Lead" who guides my career development, and I'm handed off onto projects to "Project Leads" who guide the day to day. And I use the word guide intentionally. When I'm staffed to a project, my role as a project member is to look for the project lead for finance and schedule and PM direction, and maybe to a principal consultant if there is one to guide technical direction, but I'm an IC and expected to do my work. My People lead solicits feedback from those I work with, the project leads etc. But is disconnected from my day to day, so there's no feeling of power, just a willingness to help me with my goals.

I am doubtful. If the managers are writing the performance reviews, they are not in a supporting function at all. They are the arbiters of the subordinate's success in the company and that is a vertical relationship.