Transparent oxide semiconductors are pivotal for optoelectronic applications, but the development of $p$-type ones, especially those with ultrawide band gaps, remains a significant challenge. Recently, spinel $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ (band gap approximately 5.3 eV) was reported as a robust $p$-type ultrawide band gap semiconductor, with oxygen vacancies proposed to play an important role in achieving the $p$-type conductivity. This work presents a critical first-principles reevaluation of the feasibility of $p$-type conduction in $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$. We find that, similar to its structural analog spinel $\mathrm{ZnG}{\mathrm{a}}_2{\mathrm{O}}_4$ and precursor β-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3, \mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ exhibits a deep, localized valence band maximum composed solely of O $2p$ orbitals, which intrinsically impedes hole generation and transport. Our analysis reveals that oxygen vacancies act as deep donors rather than shallow acceptors, directly invalidating the proposal that they play an important role in $p$-type conductivity. The Ga-on-Li antisite donor exhibits negative formation energies in the $p$-type Fermi level ($E_{\mathrm{F}}$) region, triggering a strong autocompensation mechanism that pins the $E_{\mathrm{F}}$ above midgap and fundamentally prohibits $p$-type conductivity. Therefore, $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ is theoretically predicted not to be a viable $p$-type semiconductor. Furthermore, the relatively high conduction band minimum of $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ inherently limits its $n$-type dopability. Although substitutional Si dopant is predicted to be a shallow donor, its prohibitively high formation energy ultimately prevents the attainment of $n$-type conductivity. Consequently, $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ is established as an intrinsic insulator. This conclusion challenges recent experimental reports of $p$-type conductivity in $\mathrm{Li}{\mathrm{Ga}}_5{\mathrm{O}}_8$ and necessitates comprehensive validation for any future claims of conductivity in ultrawide band gap oxides.

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• Electrical conductivity
• Semiconductor compounds
• Wide band gap systems
• First-principles calculations