Not sure that time keeping is so 'supremely simple' in the context of all that is sometimes going on around Triz.
It's been successfully taken away from the refs in both rugby codes and imo the games are better for having independent time keepers.
With (not so) modern technology, fans and players alike are left in no doubt about how long is left and at a time when 'cheating' is increasingly commonplace that leaves one less thing for the referee to concern himself with.