are you sure about that?
divide a centimeter into 3rds.. or quarters..
then do that with a foot.
..just for one example
Yeah, 1/3 of a foot is 4 inches. You chose very conveniently. What about 1/5 of a foot (or a yard)? That's a proportion that happens to work beautifully in metric. We can pick and choose, and find both winners and losers in both systems.
Let's make this closer to equivalent... inches vs. centimeters (although at 2.54 cm to the inch, still not square on).
Divide an inch into 3rds. Whether inch or centimeter, you'll need to do some rounding on a typical ruler. 5/16-inch is under (.3125). If that stick is more finely ruled, 11/32-inch is over (0.3475), 21/64-inch (0.328125) is about as close as you'll get. Proportionally, 3 mm is not quite as close to .333 cm as any of those others. But to be fair, 1/3-inch = 8.4666... mm - close enough to interpolate 8.5 mm and be very near the mark.
The thing is, 1/3 is problematic in either system, outside 1/3 of a yard and 1/3 of a foot. I don't ever recall seeing a ruler marked with 1/3, 1/9, and 1/27 of a foot or inch. We see 1/3 on kitchen measuring cups, and just about nowhere else.
Yet, how many ounces in 1/3 cup? For that matter, How many ounces in a fifth of bourbon (hint... that's supposed to be 1/5th of a gallon, and a gallon is 128 ounces... so it ain't a round number)?
Kitchen recipes often deal in ratios, even though recipes intended for home cooks rarely draw the connection. Two parts white flour plus one part rye flour, let's say. 2:1 ratios of that sort lead to marking measuring cups into thirds. 3:1 is another favorite among cooks - 1 teaspoon (0.5 oz) of salt plus 1 tablespoon (1.5 oz) of baking powder... and so it goes. Why do they call it pound cake? one pound each of flour, butter, sugar, and eggs. Any pound cake recipe that uses measures of volume rather than weight requires some real adaptation.
The truth is, quantities in most home recipes are rounded to the nearest convenient common measure. The optimal flavor/texture might actually be found somewhere in the gaps. You won't find many home recipes that call for 5 ounces of anything, because not every one-cup measure is marked in one-ounce increments - some are only marked in quarter-cups, others not at all. That's part of the secret of "industrial-size" recipes. The larger the quantities, the easier it is to measure-out the perfect proportions.
There are lots of custom-purpose measuring devices. In the U.S., carpenter's tape measures have a prominent mark every 16 inches, as that's the standard spacing between wall studs (and floor joists).
I have a ruler marked in picas, dating back to the days of "real" typesetting (1 pica = 1/6-inch, 12 points = 1 pica). That would come in handy for that 1/3-inch example (above). All you need to know is two picas = 1/3-inch.
We're an inventive, tool-making species, and we fashion our tools to suit the job.