Several models have been advanced to explain the multiple stellar populations observed in globular clusters (GCs). Most models necessitate a large initial population of unenriched stars that provide the pollution for an enriched population, and which are subsequently lost from the cluster. This scenario generally requires clusters to lose $>90$ per cent of their birth mass. We use a suite of 25 cosmological zoom-in simulations of present-day Milky Way-mass galaxies from the emosaics project to study whether dynamical disruption by evaporation and tidal shocking provides the necessary mass loss. We find that GCs with present-day masses $M>10^5~M_{odot}$ were only $2$-$4$ times more massive at birth, in conflict with the requirements of the proposed models. This factor correlates weakly with metallicity, gas pressure at birth, or galactocentric radius, but increases towards lower GC masses. To reconcile our results with observational data, either an unphysically steep cluster mass-size relation must be assumed, or the initial enriched fractions must be similar to their present values. We provide the required relation between the initial enriched fraction and cluster mass. Dynamical cluster mass loss cannot reproduce the high observed enriched fractions nor their trend with cluster mass.
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