It depends on if some significant chunk of the population naturally can't function on a regular basis and caffeine solves that or if caffeine withdrawals cause

It depends on if some significant chunk of the population naturally can't function on a regular basis and caffeine solves that or if caffeine withdrawals cause someone to be unable to function until they get the next dose. If it's withdrawals then caffeine is creating the problem that it later solves, which means that consuming it regularly is not a net productivity gain over not using or using rarely.