Background: Cochlear implants (CIs) are transformative neuroprosthetics that restore speech perception for individuals with severe-to-profound hearing loss. However, temporal envelope cues are well-represented within the signal processing, while spectral envelope cues are poorly accessed by CI users, resulting in substantial deficits compared to normal-hearing individuals. This profoundly impairs the perception of complex auditory stimuli like music and vocal prosody, significantly impacting users’ quality of life, social engagement, and artistic expression. Methods: This narrative review synthesizes research on CI signal-processing limitations, perceptual and production challenges in music and singing, the role of the auditory–motor feedback loop, and strategies for improvement, including rehabilitation, technology, and the influence of neuroplasticity and sensitive developmental periods. Results: The degraded signal causes marked deficits in pitch, timbre, and vocal emotion perception. Critically, this impoverished input functionally breaks the high-fidelity auditory–motor feedback loop essential for vocal control, transforming it from a precise fine-tuner into a gross error detector sensitive only to massive pitch shifts (~6 semitones). This neurophysiological breakdown directly causes pervasive pitch inaccuracies and melodic distortion in singing. Despite these challenges, improvements are possible through advanced sound-processing strategies, targeted auditory–motor training that leverages neuroplasticity, and capitalizing on sensitive periods for auditory development. Conclusions: The standard CI signal creates a fundamental neurophysiological barrier to singing. Overcoming this requires a paradigm shift toward holistic, patient-centered care that moves beyond speech-centric goals. Integrating personalized, music-based rehabilitation with advanced CI programming is essential for improving vocal production, fostering musical engagement, and ultimately enhancing the overall quality of life for CI users.