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Heterogeneous photocatalysis has been studied with various semiconductor materials for the efficient degradation of various water pollutants; however, there is the challenge of wide-bandgap photocatalyst materials, which limits their application under visible-light irradiation. Herein, a ZnO@MgO core–shell nanocomposite was synthesized using co-precipitation and applied to the photocatalytic degradation of MB dye under visible-light irradiation. MB degradation was optimized using the response surface methodology, resulting in 95.948% and ≈91% predicted and actual MB removals, respectively, at a 10 mg/L MB concentration, 1000 mg/L catalyst dose, pH 10, and time of 115.7 min. The degradation kinetics were studied, and it was found that the degradation followed pseudo-first-order kinetics with a rate constant of k = 0.07593 min⁻¹. A cost–benefit analysis was undertaken, and the operating costs were estimated based on the optimized conditions at $7.6/m³ with a payback period of 3.2 years.