Vacancy assisted atomic self-diffusion is a major structural thermalization mechanism in bulk metal alloys. Depending on alloy composition, the local atomic environments might stabilize vacancies to such extent that the vacancies become trapped and the atomic self-diffusion part of the thermalization process stalls. The consequence is that such alloys get kinetically trapped in disordered structures. In this study, we investigate equimolar AgAu, CuPt, AgPdPtIr, and AgAuCuPdPt alloy thermalizing using Metropolis Monte Carlo simulations in two approaches, one where the alloy structure changes through vacancy migration and one where the structure changes by swapping atomic pairs. By comparing the two approaches, we find that the vacancy is less effective at thermalizing alloys with more elements (i.e. AgPdPtIr and AgAuCuPdPt), more heterogeneous configurational internal energy distributions (i.e. CuPt and AgPdPtIr), and strong interactions between certain elements, e.g. Ir-Ir interactions in AgPdPtIr. In the case of AgPdPtIr, the vacancy cannot thermalize Ir-Ir neighbors even when the vacancy is mobile, because the vacancy has difficulty breaking individual Ir-Ir pairs apart.