2nd of October seems the same as intuitive as October 2nd to me.
For whatever reason, I know that one mile is 1760 yards or 5280 feet, but difficulty comes when doing anything with those numbers (e.g. How many yards in 5.2 miles? How many meters in 5.2 km? One is definitely easier to do). Maybe my chosen vocation of Engineering means I encounter unit conversions more frequently than most people. I dislike the weird combination of gauge vs 1/xths of an inch that pops up time to time (drill and screw diameters). I don’t see how one mile is more intuitive than one kilometre as a distance.
I’m not sure about the meter vs yard, they are almost the same in terms of intuitiveness as well as actual value.
I just took a measurement of my fingers and my little finger nail is about a cm wide and my foreknuckle and index knuckle separation is about an inch.
I use inches in wargaming because I grew up with warhammer miniatures which classically come on 25 mm bases, though they’re switching to 30 mm to increase the size of infantry miniatures. At a certain point there’s a balance between battlefield resolution and readability, which 25 mm bases seem fine for.
Weights are even more baffling. I think I know what an ounce is, but I hate trying to multiply it out when Americans say something is 14 ounces or something.
I know what pints are because of beer.
Temperature is annoying for both because you have to find the little symbol not present on my keyboard.