Latent-heat thermophotovoltaic (TPV) batteries are a promising approach for long-duration energy storage and dispatchable renewable power generation. Their scalability, however, is limited by the low thermal conductivity of most high-temperature phase change materials (PCMs), particularly during discharge when a solid crust forms and impedes heat transfer. This work presents an idealized theoretical analysis of a TPV battery architecture employing optically transparent PCMs, which enable both conductive and radiative heat transfer through the storage medium. A quasi-one-dimensional model is developed to simulate the thermal and electrical behavior of systems with opaque, fully transparent, and phase-dependent-transparency PCMs. Under the simplifying assumptions of perfect transparency and ideal blackbody radiation, results show that transparency markedly enhances emitter temperatures and power output, especially in the later stages of discharge, by alleviating the thermal bottlenecks associated with solidification. Moreover, transparent PCMs allow for the use of thicker storage layers without degrading performance, effectively decoupling system efficiency from storage capacity. While based on idealized assumptions, these findings establish an upper performance bound and underscore the transformative potential of radiatively transparent PCMs, motivating future experimental efforts to identify and characterize real high-temperature PCMs with partial or phase-dependent transparency under operational conditions.