We examine various implications from a dynamical and chemical model of globular clusters (GCs), which successfully reproduces the observed abundance patterns and the multiple populations of stars in these systems assuming chemical enrichment from fast-rotating massive stars. Using the model of Decressin et al., we determine the ratio between the observed, present-day mass of GCs and their initial stellar mass as a function of the stellar initial mass function (IMF). We also compute the mass of low-mass stars ejected and the amount of hydrogen ionizing photons emitted by the proto-GCs. Typically, we find that the initial masses of GCs must be ∼8–10 times (or up to 25 times, if second-generation stars also escape from GCs) larger than the present-day stellar mass. The present-day Galactic GC population must then have contributed to approximately 5–8 per cent (10–20 per cent) of the low-mass stars in the Galactic halo. We also show that the detection of second-generation stars in the Galactic halo, recently announced by different groups, provides a new constraint on the GC IMF (GCIMF). These observations appear to rule out a power-law GCIMF, whereas they are compatible with a lognormal one. Finally, the high initial masses also imply that GCs must have emitted a large amount of ionizing photons in the early Universe. Our results reopen the question on the IMF of GCs and reinforce earlier conclusions that old GCs could have represented a significant contribution to reionize the intergalactic medium at high redshift.