Non-parametric morphology measures are a powerful tool for identifying galaxy mergers at low redshifts. We employ cosmological zoom simulations using Gizmo with the Mufasa feedback scheme, post-processed using 3D dust radiative transfer into mock observations, to study whether common morphological measures Gini G, M20, concentration C, and asymmetry A are effective at identifying major galaxy mergers at z ~ 2 - 4, i.e. Cosmic Noon. Our zoom suite covers galaxies with 10^8.6 < M_* < 10^11 M_sun at z ~ 2, and broadly reproduces key global galaxy observations. Our primary result is that these morphological measures are unable to robustly pick out galaxies currently undergoing mergers during Cosmic Noon, typically performing no better than a random guess. This improves only marginally if we consider whether galaxies have undergone a merger within the last Gyr. When also considering minor mergers, galaxies display no trend of moving towards the merger regime with increasing merger ratio. From z = 4 -> 2, galaxies move from the non-merger towards the merger regime in all statistics, but this is primarily an effect of mass: Above a given noise level, higher mass galaxies display a more complex outer morphology induced by their clustered environment. We conclude that during Cosmic Noon, these morphological statistics are of limited value in identifying galaxy mergers.
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