routines for superconducting qubits has been assignment fidelity. However, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multi-qubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as an alternative and more comprehensive benchmark for single- and multi-qubit readout optimization. We find the most effective allocation of a fixed shot budget between detector tomography and state reconstruction in single- and two-qubit experiments. To address the growing interest in three-qubit gates, we perform three-qubit quantum state tomography that goes beyond conventional readout error mitigation methods and find a factor of 30 reduction in quantum infidelity. Our results demonstrate that neither quantum nor classical qubit readout correlations are induced even by very high levels of readout noise. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.