All in all I prefer the SI system, but the Imperial system has it's advantages. 5280 feet seems really arbitrary, but can halve it five times and still get an integer.
It also divides evenly by 3.
For comparison:
1/3 of a mile is 1760 feet. 1/2 of that is 880 feet 1/2 of that is 440 feet 1/2 of that is 220 feet 1/2 of that is 110 feet 1/2 of that is 55 feet.
1/3 of a km is 333.333333 meters 1/2 of that is 166.666667 meters 1/2 of that is 83.333333 meters 1/2 of that is 41.666667 meters 1/2 of that is 20.833333 meters 1/2 of that is 10.416667 meters