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ABSTRACT Microbial host populations evolve traits conferring specific resistance to viral predators via various defence mechanisms, while viruses reciprocally evolve traits to evade these defences. Such coevolutionary dynamics often involve diversification promoted by negative frequency‐dependent selection. However, microbial traits conferring competitive asymmetries can induce directional selection, opposing diversification. Despite extensive research on microbe–virus coevolution, the combined effect of both host trait types and associated selection remains unclear. Using a CRISPR‐mediated coevolutionary system, we examine how the co‐occurrence of both trait types impacts viral evolution and persistence, previously shown to be transient and nonstationary in computational models. A stochastic model incorporating host competitive asymmetries via variation of intrinsic growth rates reveals that competitively advantaged host clades generate the majority of immune diversity. Greater asymmetries extend viral extinction times, accelerate viral adaptation locally in time and augment long‐term local adaptation. These findings align with previous experiments and provide further insights into long‐term coevolutionary dynamics.