Bacterial communities are often highly diverse with several closely related species (or strains) coexisting together. These bacteria compete for resources and the competitive exclusion principle predicts that all but the fastest-growing bacteria will go extinct. When exposed to phage, it is predicted that bacterial strains with restriction-modification (RM) systems can circumvent the competitive exclusion principle and reach diversity of the order of the phage burst size. We show that with a trade-off between bacterial growth rates and the strength of their RM systems, the diversity of such an ecosystem can further increase several fold beyond the burst size limit. Moreover, we find that the ratio of the growth rate of a bacterial strain to the imperfection of its RM system is an excellent predictor of (i) whether the strain will go extinct or not, and (ii) the biomass of the strain if it survives. In contrast, the growth rate alone is not a determinant of either of these properties. Our work provides a quantitative example of a model ecosystem where the fitness of a species is determined not by growth rate, but by a trade-off between growth and defence against predators.