Single-atom catalysts have attracted a significant amount of attention due to their exceptional atomic utilization and high efficiency in a range of catalytic reactions. However, these systems often face thermodynamic instability, leading to agglomeration under the operational conditions. In this study, we investigate the interactions of 12 types of catalytic atoms (Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt, Au, and Bi) on three crystalline phases (1T, 1T', and 2H) of six transition metal dichalcogenide layers (MoS2, MoSe2, MoTe2, WS2, WSe2, and WTe2) using first-principles calculations. We ultimately identify 82 stable single-atom systems that thermodynamically prevent the formation of metal clusters on these substrates. Notably, our findings reveal that the metastable 1T and 1T' phases significantly enhance the binding strength with single atoms and promote their thermodynamic stability. This research offers valuable insights into the design of stable single-atom systems and paves the way for the discovery of innovative catalysts.