The protagonists of the last great phase transition of the universe-cosmic reionization-remain elusive. Faint starforming galaxies are leading candidates because they are found to be numerous and may have significant ionizing photon escape fractions ( fesc). Here we update this picture via an empirical model that successfully predicts latest observations (e.g., the rapid drop in star-formation density (rSFR at z > 8). We generate an ionizing spectrum for each galaxy in our model and constrain fesc by leveraging latest measurements of the reionization timeline (e.g., Lya damping of quasars and galaxies at z.>.7). Assuming a constant fesc across all sources at z.>.6, we find MUV..8.SFR and favored by high neutral fractions (60%-90%) measured at z..7-8. Inspired by the emergent sample of Lyman Continuum (LyC) leakers spanning z..0-6.6 that overwhelmingly displays higher-than-average star-formation surface density (SSFR), we propose a physically motivated model relating fesc to SSFR and find fesc mu S. SFR0.4 0.1. Since SSFR falls by 2.5 dex between z.=.8 and z.=.0, our model explains the humble upper limits on fesc at lower redshifts and its required evolution to fesc..0.2 at z.>.6. Within this model, strikingly, .8 (the "oligarchs") account for..80% of the reionization budget-a stark departure from the canonical "democratic" reionization led by copious faint sources. In fact, faint sources (MUV.>. -16) must be relegated to a limited role in order to ensure high neutral fractions at z.=.7-8. Shallow faint-end slopes of the UV luminosity function (aUV.>.-2) and/or fesc distributions skewed toward massive galaxies produce the required late and rapid reionization. We predict that LyC leakers like COLA1 (z.=.6.6, fesc..30%, MUV.=.-21.5) will become increasingly common toward z..6 and that the drivers of reionization do not lie hidden across the faint end of the luminosity function but are already known to us.