Constraining the astrophysics of galaxy formation and the fundamental physics of cosmology requires large sky surveys of both galaxies and the diffuse gaseous cosmic web. Large-volume galaxy population models are crucial for interpreting data from these surveys, but all such models have limited predictive power owing to their phenomenological nature. I will describe my recent work on re-tooling semi-analytic models (SAMs) of galaxy formation to emulate cosmological hydrodynamical "zoom-in" simulations with the goal of realizing the full potential of both modeling approaches. Both techniques predict remarkably similar stellar mass assembly histories for galaxies but dramatically different underlying gas flow cycles. Dwarf galaxies in SAMs have orders of magnitude higher gas flow rates and much lower circumgalactic medium (CGM) masses compared to the simulations. I argue that these discrepancies are caused by the lack of "preventative feedback" in SAMs. I present a simple model in which energy-conserving winds are allowed to shock-heat some fraction of circumgalactic and intergalactic gas to above the halo virial temperature, effectively preventing accretion as seen in the simulations. Finally, I will discuss a few remaining missing pieces in the standard model of halo gas accretion, cooling and recycling whose inclusion in SAMs will allow us to fully leverage the growing wealth of data on the CGM - galaxy connection.