Quantum cascade lasers (QCLs) facilitate compact optical frequency comb sources that operate in the mid-infrared and terahertz spectral regions, where many molecules have their fundamental absorption lines. Enhancing the optical bandwidth of these chip-sized lasers is of paramount importance to address their application in broadband high-precision spectroscopy. In this work, we provide a numerical and experimental investigation of the comb spectral width and show how it can be optimized to obtain its maximum value defined by the laser gain bandwidth. The interplay of nonoptimal values of the resonant Kerr nonlinearity and cavity dispersion can lead to significant narrowing of the comb spectrum and reveals the best approach for dispersion compensation. The implementation of high mirror losses is shown to be favorable and results in proliferation of the comb sidemodes. Ultimately, injection locking of QCLs by modulating the laser bias around the round trip frequency provides a stable external knob to control the frequency-modulated comb state and recover the maximum spectral width of the unlocked laser state.