Present-day clusters are massive halos containing mostly quiescent galaxies, while distant protoclusters are extended structures containing numerous star-forming galaxies. We investigate the implications of this fundamental change in a cosmological context using a set of N-body simulations and semi-analytic models. We find that the fraction of the cosmic volume occupied by all (proto)clusters increases by nearly three orders of magnitude from z=0 to z=7. We show that (proto)cluster galaxies are an important, and even dominant population at high redshift, as their expected contribution to the cosmic star-formation rate density rises (from 1% at z=0) to 20% at z=2 and 50% at z=10. Protoclusters thus provide a significant fraction of the cosmic ionizing photons, and may have been crucial in driving the timing and topology of cosmic reionization. Internally, the average history of cluster formation can be described by three distinct phases: at z~10-5, galaxy growth in protoclusters proceeded in an inside-out manner, with centrally dominant halos that are among the most active regions in the Universe; at z~5-1.5, rapid star formation occurred within the entire 10-20 Mpc structures, forming most of their present-day stellar mass; at z<~1.5, violent gravitational collapse drove these stellar contents into single cluster halos, largely erasing the details of cluster galaxy formation due to relaxation and virialization. Our results motivate observations of distant protoclusters in order to understand the rapid, extended stellar growth during Cosmic Noon, and their connection to reionization during Cosmic Dawn.