Halide double perovskites are increasingly recognized as promising substitutes for conventional lead-based absorber materials due to their improved chemical stability, reduced environmental impact, and adjustable optoelectronic characteristics. In this study, solar cells with the architecture FTO/TiO₂/Cs₂MI₆/PEDOT:PSS/Ag were simulated using SCAPS-1D, where the M-site cation was systematically varied among Ti, Sn, Pt, and Te. The influence of ionic radius, electronegativity, oxidation state, and electronic configuration on photovoltaic performance was investigated through thickness-dependent simulations, energy-level alignment, carrier generation–recombination profiles, and impedance spectroscopy. Results reveal that Cs₂PtI₆ achieves the highest efficiency (30.72% at 600 nm), which we attribute to its favorable electronic properties, strong Pt–I covalent bonding, wide band gap, and suppressed recombination as established by previous DFT and experimental studies and used as input parameters in our SCAPS-1D model. This value is consistent with recent numerical predictions for optimized Cs₂PtI₆ devices. Cs₂SnI₆ exhibits stable performance across a broad thickness range, with a plateau efficiency of ∼20.5%. Cs₂TiI₆ shows a narrow optimum thickness window (19.18% at 250 nm) limited by bulk recombination, while Cs₂TeI₆ requires thicker absorbers to reach ∼19.8% efficiency due to reduced carrier mobility. Nyquist plots confirm distinct impedance behaviors, with Cs₂PtI₆ displaying the smallest semicircle and Cs₂SnI₆ the largest, consistent with their respective recombination dynamics. By integrating systematic M-site cation engineering with impedance (Nyquist) analysis, this work advances existing numerical studies by establishing direct correlations between cation substitution, electronic structure, and device performance, offering design principles for optimizing double perovskite solar cells.