To know that 0.32 m is smaller than 43 cm I have to actively think, but I'm guessing you don't. I've never had to think about 3/4 vs 1/2. Even 5/16ths vs 1/4 is intuitive for me.
When we use fractions for measurements, the denominator is virtually always a power of two. The only one I can think of that isn't is a fifth of alcohol, which is really just its own unit at this point.
An inch is 1/36 yd or 1/12 ft or 6 pica or 72 pt. There is no power of two whatsoever in this.
Neither 1/36th or 1/12th are used, and the other two aren't fractions. We don't say six and a twelfth feet, we say six feet one inch. With distance, fractions are only used for fractions of an inch (apart from trivial uses like "one and a half miles").