Voice biomarkers--human-generated acoustic signals such as speech, coughing, and breathing--are promising tools for scalable, non-invasive detection and monitoring of mental health and neurodegenerative diseases. Yet, their clinical adoption remains constrained by inconsistent quality and limited usability of publicly available datasets. To address this gap, we present the first systematic FAIR (Findable, Accessible, Interoperable, Reusable) evaluation of 27 publicly available voice biomarker datasets focused on these disease areas. Using the FAIR Data Maturity Model and a structured, priority-weighted scoring method, we assessed FAIRness at subprinciple, principle, and composite levels. Our analysis revealed consistently high Findability but substantial variability and weaknesses in Accessibility, Interoperability, and Reusability. Mental health datasets exhibited greater variability in FAIR scores, while neurodegenerative datasets were slightly more consistent. Repository choice also significantly influenced FAIRness scores. To enhance dataset quality and clinical utility, we recommend adopting structured, domain-specific metadata standards, prioritizing FAIR-compliant repositories, and routinely applying structured FAIR evaluation frameworks. These findings provide actionable guidance to improve dataset interoperability and reuse, thereby accelerating the clinical translation of voice biomarker technologies.