Motivated by the current controversy over the redshift distribution and physical properties of luminous (sub-)mm sources, we have undertaken a new study of the brightest sample of unlensed (sub-)mm sources with pre-Atacama Large Millimeter/submillimeter Array (ALMA) interferometric follow-up in the Cosmological Evolution Survey field. Exploiting the very latest multifrequency supporting data, we find that this sample displays a redshift distribution indistinguishable from that of the lensed sources uncovered with the South Pole Telescope, with z_median_=~3.5. We also find that, over the redshift range z=~2-6, the median stellar mass of the most luminous (sub-) mm sources is M_*_=~ 3x10^11^M_{sun}_, yielding a typical specific star formation rate sSFR=~3Gyr^-1^. Consistent with recent ALMA and the Submillimeter Array studies, we confirm that source blending is not a serious issue in the study of luminous (sub-)mm sources uncovered by ground-based, single-dish surveys; only =~10^-15^% of bright (S_850_=~5-10mJy) (sub-) mm sources arise from significant (i.e. >20%) blends, and so our conclusions are largely unaffected by whether we adopt the original single-dish mm/sub-mm flux densities/positions or the interferometric data. Our results suggest that apparent disagreements over the redshift distribution of (sub-)mm sources are a result of 'down-sizing' in dust-enshrouded star formation, consistent with existing knowledge of the star formation histories of massive galaxies. They also indicate that extreme star-forming galaxies at high redshift are, on average, subject to the same star formation rate-limiting processes as less luminous objects, and lie on the 'main sequence' of star-forming galaxies at z>3.