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We present a theoretical analysis of mid-infrared radiative recombination in InAs/GaSb superlattices (SLs). We employ a semi-analytical plane wave expansion method in conjunction with an 8-band $\mathbf{k} \cdot \mathbf{p}$ Hamiltonian to compute the SL electronic structure, paying careful attention to the identification and mitigation of spurious solutions. The calculated SL eigenstates are used directly to compute spontaneous emission spectra and the radiative recombination coefficient $B$. We elucidate the origin of the relatively large $B$ coefficients in InAs/GaSb SLs which, despite the presence of spatially indirect (type-II-like) carrier confinement, are close to that of bulk InAs and compare favourably to those calculated for mid-infrared type-I pseudomorphic and metamorphic quantum well structures having comparable emission wavelengths. Our analysis explicitly quantifies the roles played by carrier localisation (specifically, partial delocalisation of bound electron states) and miniband formation (specifically, miniband occupation and optical selection rules) in determining the magnitude of $B$ and its temperature dependence. We perform a high-throughput optimisation of the room temperature $B$ coefficient in InAs/GaSb SLs across the 3.5 -- 7 $\mu$m wavelength range, quantifying the dependence of $B$ on the relative thickness of the electron-confining InAs and hole-confining GaSb layers. This analysis provides guidance for the growth of optimised SLs for mid-infrared light emitters. Our results, combined with the expected low non-radiative Auger recombination rates in structures having spatially indirect electron and hole confinement, corroborate recently observed high output power in prototype InAs/GaSb SL inter-band cascade light-emitting diodes., Comment: Published version