What annoys me is that the US gets singled out when the difference is one of degree, not kind. The UK still uses pints for beers, most countries still use their equivalent to feet in carpentry.
In what real life situation would you want to divide 1 foot by 3 and get an integer as the result? If you're cutting materials, you usually want a given length, not 1/3 of whatever you happen to already have. So you're doing addition and subtraction, not division.
Also, it only works when you're simultaneously converting from feet to inches, and only when it's 1 foot! It's no use dividing 1 inch by 3, or 10 feet by 3 or almost any other length really. Though you could do a little maths to get 2 feet / 3 = 8 inches. But 4 feet / 3 isn't called 16 inches, it's 1 foot 4 inches which is pretty complicated to work out compared to ordinary decimal maths.
4 feet divided by 3
= 4 * 4 inches
= 16 inches (It's perfectly reasonable to stop here, your tape measure isn't going only say 1'4")
= 16/12 feet + 16%12 inches
= 1'4"
vs.
4 meters divided by 3
= 4/3meters + ...
= 1meter + 4%3/0.3 decimeters
= 1.3meter + 4%0.3/0.03 centimeters
= 1.33meters ...
For each level of precision in metric you have to remember one additional digit, where as in the degenerate case for imperial you remember a constant number of digits at each step. Think of it as making multiples of the {1,1,2}th primes more convenient vs making the {1,3}th primes more convenient.
But I still doubt this has any practical use. Can you give me a concrete example where you or anybody you know has done this? How common is it?
Can we agree that equally spacing 4 of something is a common operation? The metric example would be, 2 meters, divided by 3 = 0.333x2m = 0.666m But look at your tape measure and see which measurement is marked more promimently, an arbitrary centimeter precision measurement or an integer number of inches.
30cm divides as well as 12in, and things that aren't nice numbers are easier to handle in cm or mm. Mark out every 4⅝ inches until you have a yard, then mark out every 12mm.
Contrived examples are easy.
You know what also doesn't make sense? The SI Prefix system, where you have redundancies like "A thousand megawatts" instead of just saying "A billion watts". Most languages already have built in prefix systems. In fact, South and East Asian languages space theirs every 10^4 instead of 10^3, making SI prefixes a clusterfuck to use. That's in addition to the fact that the prefixes themselves are chosen haphazardly. The ordering of Micro, Nano, and Pico has no discernible pattern as most people simply know all three words to mean small. Abbreviations such as M, m, and μ, are easily mixed up.
Contrast that to thou and mil, which are easily remembered as abbreviations of thousandth and millionth. It's also easily extendable to an arbitrary precision.