Frequency-modulated (FM) combs form spontaneously in free-running semiconductor lasers and possess a vast potential for spectroscopic applications. Despite recent progress in obtaining a conclusive theoretical description, experimental FM combs often exhibit non-ideal traits, which prevents their widespread use. Here we explain this by providing a clear theoretical and experimental study of the impact of the higher-order dispersion on FM combs. We reveal that spectrally dependent dispersion is detrimental for comb performance and leads to a decreased comb bandwidth and the appearance of spectral holes. These undesirable traits can be mended by applying a radio frequency modulation of the laser bias. We show that electrical injection-locking of the laser leads to a significant increase of the comb bandwidth, a uniform-like spectral amplitudes, and the rectification of the instantaneous frequency to recover a nearly linear frequency chirp of FM combs.