A-Site doping with alkali ions, and/or metal substitution at the B and B'-sites, are among the key strategies in the innovative development of A 2BB'X6 halide double perovskite semiconducting materials for application in energy and device technologies. To this end, we have investigated an intriguing series of five halide-based non-toxic systems, A 2AgRhCl6 (A = Li, Na, K, Rb, and Cs), using density functional theory at the SCAN-rVV10 level. The lattice stability and bonding properties emanating from this study of A 2AgRhCl6 matched well with those that have already been synthesized, characterized and discussed [viz. Cs2AgBiX6 (X = Cl, Br)]. Exploration of traditional and recently proposed tolerance factors has enabled us to identify A 2AgRhCl6 (A = K, Rb and Cs) as stable double perovskites. The band structure and density of states calculations suggested that the electronic transition from the top of the valence band [Cl(3p)+Rh(4d)] to the bottom of the conduction band [(Cl(3p)+Rh(4d)] is inherently direct at the X-point of the first Brillouin zone. The (non-spin polarized) bandgap of these materials was found in the range 0.57-0.65 eV with SCAN-rVV10, which were substantially smaller than those computed with hybrid HSE06 and PBE0, and quasi-particle GW methods. This, together with the appreciable refractive index and high absorption coefficient in the region covering the range 1.0-4.5 eV, enabled us to demonstrate that A 2AgRhCl6 (A = K, Rb, and Cs) are likely candidate materials for photoelectric applications. The results of our phonon calculations at the harmonic level suggested that the Cs2AgRhCl6 is the only system that is dynamically stable (no imaginary frequencies found around the high symmetry lines of the reciprocal lattice), although the elastic moduli properties suggested all five systems examined are mechanically stable.