Background/Objectives: Music is an important component of quality of life and is increasingly recognized as a meaningful patient-centered outcome in hearing healthcare. Although individuals with hearing loss frequently report reduced enjoyment of music, research in this area has focused on auditory perception, including pitch, timbre, melody, and sound quality. Consequently, music enjoyment is often conceptualized and measured primarily through perceptual performance, despite growing evidence that enjoyment represents a broader subjective experience. Methods: This narrative review examines the current conceptualization of music enjoyment in individuals with hearing loss by integrating literature from audiology, music psychology, affective neuroscience, and patient-reported outcome measurement. Results: We discuss music enjoyment as a multidimensional construct influenced by, but not limited to, auditory perception. Additional determinants include emotional reward, musical engagement, prior musical experience, expectations, identity, listening behaviors, and social context. We further examine evidence demonstrating that music perception and music enjoyment, while related, may diverge substantially across individuals with hearing loss, highlighting the limitations of equating perceptual fidelity with patient experience. Finally, we consider the implications of this conceptual distinction for hearing rehabilitation and music-related outcome measurement. Conclusions: We argue that a broader patient-centered understanding of music enjoyment is necessary to guide future research, inform clinical practice, and support the development of next-generation patient-reported outcome measures capable of capturing the complexity of music experience in individuals with hearing loss.