I work within a consulting organization which carries out project work for clients. We have a matrix structure - one (weak) structure is staff management, and the (more meaningful) structure is client and project management. There are many aspects of the matrix structure that don't work, but what would be better?
To go into more detail, the company I work for has a number of practices, each led by a practice leader, each with about 25 people. They each have about 6 DRs, some of whom are managers, who in turn have up to about 6 DRs. The managers are responsible for the hiring, firing, reviews and salaries of their DRs, but the manager and their DRs don't actually make up a team that owns any work. In reality the practice leader retains most of the responsibility and it's difficult to delegate it out efficiently.
Overlaid on this is the project structure. Each project has a project manager, who often has a team of perhaps 5 people working for them, mostly full-time, and mostly for several months. The PM is responsible for the day-to-day work of each of their team on a very real basis. This structure has much more actual meaning for most people, although organizationally has less official power. However, it's a fluid structure, as projects start and finish, and as people move between projects.
I'm both a manager and a project manager. From the perspective of allowing me to manage people effectively, being a project manager is great. The roles and objectives of me and the project team are clear, and I can do lots of good MT trinity things. Being a staff manager is much more challenging. It frankly feels much more like a mentorship relationship. I still do O3s, and some of the rest, but it's rather insubstantial.
My main question here is that clearly the matrix structure is creating some challenges, but what would be better? Should we have 25 people reporting directly to the practice leader? We could in theory have managers and teams grouped around particularly responsibilities, but I don't see any natural groupings that would provide much more 'meat' to the roles than now. Should we give more formal power to the PMs? But if so, how do we handle the fluidity of that?