The breadth of pathogens to which T cells can respond is determined by the T cell receptors (TCRs) present in an individual’s repertoire. Although more than 90% of the sequence diversity among TCRs is generated by terminal deoxynucleotidyl transferase (TdT)-mediated N-nucleotide addition during V(D)J recombination, the benefit of TdT-altered TCRs remains unclear. Here, we computationally and experimentally investigated whether TCRs with higher N-nucleotide diversity via TdT make distinct contributions to acute or chronic pathogen control specifically through the inclusion of TCRs with lower antigen binding strengths (i.e., lower reactivity to peptide-major histocompatibility complex (pMHC)). When T cells with high pMHC reactivity have a greater propensity to become functionally exhausted than those of low pMHC reactivity, our computational model predicts a shift toward T cells with low pMHC reactivity over time during chronic, but not acute, infections. This TCR-affinity shift is critical, as the elimination of T cells with lower pMHC reactivity in silico substantially increased the time to clear a chronic infection, while acute infection control remained largely unchanged. Corroborating an affinity-centric benefit for TCR diversification via TdT, we found evidence that TdT-deficient TCR repertoires possess fewer T cells with weaker pMHC binding strengths in vivo and showed that TdT-deficient mice infected with a chronic, but not an acute, viral pathogen led to protracted viral clearance. In contrast, in the case of a chronic fungal pathogen where T cells fail to clear the infection, both our computational model and experimental data showed that TdT-diversified TCR repertoires conferred no additional protection to the hosts. Taken together, our in silico and in vivo data suggest that TdT-mediated TCR diversity is of particular benefit for the eventual resolution of prolonged pathogen replication through the inclusion of TCRs with lower foreign antigen binding strengths.