"Current or recent" goes back a long way. The US army was using maps marked in kilometers in WWI, so if you're still breathing and served in the infantry or artillery, you probably used meters.
The US Navy still measures distances in nautical miles, gun diameter in inches and gun length in calibers. Both military and civil aviation, not just in the US but also internationally in civil aviation, still use feet for altitude and knots for airspeed.
Our military's use of the metric system is also a bit of a misuse of the metric system, since recruits come in thinking in inches and yards. As a result, recruits are still taught to estimate distances with methods such as "estimating the number of football fields", and they are not talking soccer, but rather American football. So in effect, they are taking distances familiar to Americans and grafting them on to the metric system.
Ranging formulas for shooting in the military work pretty well, but it's a very simplified system. For example the average distance between waist and top of helmet is assumed to be 1 meter. So if a 1 meter tall target subtends 2 mils in a mil-dot or mil-hash reticle the formula is pretty simple:
1 meter / 2 mils = 0.5, 0.5 x 1000 = 500 meters.
3 mils, and it's 333 meters.
1.5 mils and it's 666 meters.
Shoulder to shoulder width is assumed to be 1/2 meter, so:
.5 meters / 2 mils = 250 meters.
But since it's harder for people to work with .5 in the numerator, they just adjust the formula so that you use 1 again, but with 500 rather than 1000 on the end:
1 unit / 2 mils = .5, and .5 x 500 = 250 meters
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Of course the same thing works in inches as well:
target size in inches / target subtension in MOA x 100 = range to target in yards.
36" / 6 MOA = 6, and 6 x 100 = 600 yards.
18" / 4 MOA = 4.5, and 4.5 x 100 = 450 yards.
Technically it's 95.5 rather than 100, but estimating target size +/- 4.5% isn't realistic in the real world so the rounding error isn't the limiting factor.
The point here is that the US military uses klicks for commonality with our NATO allies for mapping purposes and artillery fire direction purposes since it's map dependent, and our troops use meters as a stand in for yards. However, most US shooters, even those with military backgrounds, tend to think in terms of target sizes in inches and range to targets in yards and would actually be better served using imperial units (inches and yards) and MOA rather than Mil. But it's really hard to get many of them to admit that as meters and mils sound cooler and is "mil-spec".