Seriously though good question. First though it made me realize that you never see prices in thirds of a dollar- as if everyone avoids it and have simply gotten used to avoiding it. I can't imagine a situation where ease of dividing by three for money actually adds any efficiency. Similarly, while I do see the value in dividing the day into 24 hours, I certainly wouldn't advocate a unit that's defined as one 60th of a second (even though it has even more prime factors than 12 ;)
I concede that the use-cases where having more prime factors and therefore easy non-decimal division are few and far between. I guess what surprised me when doing construction was that there was a very rational reason for a foot being 12 inches rather than 10- that it's not simply a relic of the fact that a human foot seems to be about 12 thumbs long- some arbitrary number accidentally ingrained in some cultures. And as illustrated by the fact that stocks were eventually decimalized and then made to trade at penny-granularity, computers and the fact that we don't do a lot of division in our heads or on paper anymore will probably eventually erase most remaining efficiencies.