Deep surveys with the James Webb Space Telescope (JWST) have revealed an emergent population of moderate-luminosity, broad-line active galactic nuclei (AGNs) at 4 âČ z âČ 13 powered by accretion onto early massive black holes. The high number densities reported, together with the large Lyman-continuum (LyC) production efficiency and leakiness into the intergalactic medium that are typical of UV-selected AGNs, lead us to reassess a scenario where AGNs are the sole drivers of the cosmic hydrogen/helium reionization process. Our approach is based on the assumptions, grounded in recent observations, that (a) the fraction of broad-line AGNs among galaxies is around 10%â15%; (b) the mean escape fraction of hydrogen LyC radiation is high, at âł80%, in AGN hosts and is negligible otherwise; and (c) internal absorption at 4 ryd or a steep ionizing EUV spectrum delay full reionization of He ii until z â 2.8â3.0, in agreement with observations of the He ii Lyα forest. In our fiducial models, (1) hydrogen reionization is 99% completed by redshift z â 5.3â5.5 and reaches its midpoint at z â 6.5â6.7; (2) the integrated Thomson scattering optical depth to reionization is â0.05, consistent with constraints from cosmic microwave background anisotropy data; and (3) the abundant AGN population detected by JWST does not violate constraints on the unresolved X-ray background.