Accurate mathematical modeling allows Covid surges to be predicted and public health measures to be well-timed. Although many models exist that are able to capture Covid case trends, broad disagreements remain about how complex models must be to capture the diversity of Covid case dynamics. Here, we form clusters of Covid trajectories in U.S. states and use model-agnostic data analysis to estimate the effective population size of Covid-contracting individuals. These clusters exhibit a surprisingly small repertoire of possible case trajectories that are largely insensitive to differences in public health measures. Low levels of dynamical variation between case curve groupings suggests that the right model for capturing case trajectories may rely on only a few parameters. In turn, we revisit compartment models as the simplest models for how individuals interact and proliferate Covid. Our analysis shows why SIR models may successfully represent dynamics of disease spread even in heterogeneous populations. With this new understanding of SIR fitting in mind, we show the models predict Omicron case surges with high fidelity.