The protagonists of cosmic reionization remain elusive. Faint star-forming galaxies are leading candidates because they are numerous and may have significant ionizing photon escape fractions ($f_{esc}$). Here we update this picture via an empirical model that successfully predicts latest observations (e.g., the drop in star-formation density at z>8). We generate an ionizing spectrum for each galaxy in our model and constrain $f_{esc}$ using latest measurements of the reionization timeline (e.g., Ly$alpha$ damping of quasars and galaxies at z>7). Assuming a constant $f_{esc}$, we find $M_{UV}$<-13.5 galaxies need $f_{esc}=0.21^{+0.06}_{-0.04}$ to complete reionization. The inferred IGM neutral fraction is [0.9, 0.5, 0.1] at z=[8.2, 6.8, 6.2]$pm$0.2, i.e., the bulk of reionization transpires in 300 Myrs. Inspired by the emergent sample of Lyman Continuum (LyC) leakers that overwhelmingly displays higher-than-average star-formation surface density ($Sigma$), we propose a model relating $f_{esc}$ to $Sigma$ and find $f_{esc}proptoSigma^{0.4pm0.1}$. Since $Sigma$ falls by ~2.5 dex between z=8 and z=0, our model explains the humble upper limits on $f_{esc}$ at lower redshifts and its required evolution to ~0.2 at z>6. Within this model, strikingly, <5% of galaxies with $M_{UV}$<-18 (the `oligarchs) account for >80% of the reionization budget. In fact, faint sources ($M_{UV}$>-16) must be relegated to a limited role to ensure high neutral fractions at z=7-8. Shallow faint-end slopes of the UV luminosity function ($alpha$>-2) and/or $f_{esc}$ distributions skewed toward bright galaxies produce the required late and rapid reionization. We predict LyC leakers like COLA1 (z=6.6, $f_{esc}$~30%, $M_{UV}$=-21.5) become increasingly common towards 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. (abridged)
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