We investigate open-system charging protocols for Rabi and Dicke quantum batteries under direct incoherent pumping. The charging dynamics follows a Lindblad master equation, while effective non-Hermitian generators describe the conditioned no-jump mechanism. For a single Rabi battery, this pumping suppresses coherent energy backflow, broadens the high-energy charging window, and improves robustness against both timing errors and detuning. At the selected Rabi operating points, pumping also increases ergotropy and the extractable fraction of the stored energy. For finite Dicke batteries, direct incoherent pumping likewise stabilizes the charging dynamics. Across the finite-size scan, the strongest pump considered improves the peak stored energy and ergotropy per cell and near-peak timing robustness relative to the Hermitian reference. The maximum average charging power also increases, although this metric includes pump-assisted jump contributions. Equal-input comparisons show that the relative performance of common-cavity Dicke and independent Rabi batteries varies with the pump-input bound. Taken together, these results show that direct incoherent pumping provides a route to stabilized charging in Rabi and finite Dicke quantum batteries.

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• Open quantum systems & decoherence
• Quantum optics
• Quantum thermodynamics
• Non-Hermitian systems
• Lindblad equation
• Rabi model