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The rapid growth of rooftop photovoltaic (PV) generation and battery energy storage is increasing the number of power-electronic inverters connected to low-voltage distribution networks, creating both new power-quality challenges and an opportunity to use existing converter capacity more intelligently. Harmonic distortion, phase voltage unbalance, and limited inverter capacity can become particularly problematic in feeders with uneven single-phase loads and high penetration of converter-interfaced resources. This paper proposes a stability-constrained multi-objective dispatch framework for PV–battery smart inverters that coordinates harmonic suppression and voltage-unbalance compensation while explicitly accounting for the competition among power-quality support, inverter VA headroom, and renewable-energy yield. Rather than treating harmonic compensation, negative-sequence mitigation, and PV–battery energy management as independent functions, the proposed framework allocates the available inverter capacity among fundamental active and reactive power, harmonic compensation currents, and negative-sequence support while enforcing voltage, current, state-of-charge, thermal, and small-signal stability constraints. A Pareto-based multi-objective optimization is used to expose the trade-offs among total harmonic distortion (THD), voltage unbalance factor (VUF), required converter headroom, network losses, and curtailed PV energy. The framework is evaluated on an unbalanced low-voltage distribution feeder under time-varying PV generation, asymmetric loading, nonlinear loads, and different battery operating conditions. Simulation results show that coordinated dispatch reduces the maximum bus-voltage THD from 6.8% to 2.7% and decreases the worst-case VUF from 3.4% to 1.1%, while maintaining bus voltages within 0.95–1.05 p.u. and satisfying the imposed stability limits. Compared with power-quality-blind PV–battery operation, the selected balanced Pareto solution achieves these improvements while retaining approximately 93.6% of the baseline PV energy yield, requiring about 18.4% inverter VA headroom, and reducing feeder losses by approximately 11.7%. Moving toward the extreme minimum-THD or minimum-VUF solutions provides additional power-quality improvement but produces rapidly diminishing benefits relative to the additional converter headroom and renewable-energy curtailment required. Sensitivity studies further indicate that the balanced solution remains effective under variations in PV penetration, load asymmetry, nonlinear-load severity, battery SOC, and inverter oversizing. The results demonstrate that inverter capacity should be viewed as a dynamically allocatable grid resource rather than being reserved exclusively for active-power conversion. The main limitation is that the present assessment is simulation based and assumes sufficiently accurate network measurements and inverter models; therefore, hardware-in-the-loop and experimental validation remain necessary. Practically, the proposed framework could allow distribution operators and prosumers to improve power quality using already deployed PV–battery infrastructure, potentially reducing reliance on dedicated compensating equipment and supporting higher renewable hosting capacity. More broadly, the study provides a transparent Pareto-based basis for deciding how much renewable-energy yield and converter capacity should reasonably be exchanged for cleaner, more balanced, and more resilient low-voltage electricity networks.