The empirical upper limit to Red Supergiant (RSG) luminosity, known as the Humphreys-Davidson (HD) limit, has been commonly explained as being caused by the stripping of stellar envelopes by metallicity-dependent, line-driven winds. As such, the theoretical expectation is that the HD limit should be higher at lower metallicity, where weaker mass-loss rates mean that higher initial masses are required for an envelope to be stripped. In this work, we test this prediction by measuring the luminosity function of RSGs in M31 and comparing to those in the LMC and SMC. We find that $\[\log ({L_{{\rm{m}}ax}}/{L_ \odot }) = 5.53 \pm 0.03\]$ in M31 (Z ≳ Z⊙), consistent with the limit found for both the LMC (Z ∼ 0.5 Z⊙) and SMC (Z ∼ 0.25 Z⊙), while the RSG luminosity distributions in these 3 galaxies are consistent to within 1σ. We therefore find no evidence for a metallicity dependence on both the HD limit and the RSG luminosity function, and conclude that line-driven winds on the main sequence are not the cause of the HD limit.