We consider a user-centric scalable cell-free massive MIMO network with a total of $LM$ distributed remote radio unit antennas serving $K$ user equipments (UEs). Many works in the current literature assume $LM\gg K$, enabling high UE data rates but also leading to a system not operating at its maximum performance in terms of sum throughput. We provide a new perspective on cell-free massive MIMO networks, investigating rate allocation and the UE density regime in which the network makes use of its full capability. The UE density $K$ approximately equal to $\frac{LM}{2}$ is the range in which the system reaches the largest sum throughput. In addition, there is a significant fraction of UEs with relatively low throughput, when serving $K>\frac{LM}{2}$ UEs simultaneously. We propose to reduce the number of active UEs per time slot, such that the system does not operate at ``full load'', and impose throughput fairness among all users via a scheduler designed to maximize a suitably defined concave componentwise non-decreasing network utility function. Our numerical simulations show that we can tune the system such that a desired distribution of the UE throughput, depending on the utility function, is achieved.