Yes, the successor to the 5000-foot Roman mile should have been 5040, but 5280 isn't bad for something that arose organically out of various unit systems' needs.
Metric is not “automatic” either. One year in university I took three classes that happened to be in the same classroom. One was in cgs, one was in MKs and one in ASME units (US customary units plus mils). Three different subject domains. It didn’t feel odd or complicated.
I think most people in the US just convert the meter to the three-foot yard measure. I doubt people would notice if you did the same thing in order to give estimates in feet. I work in metric weights but speak to people using US Imperial weights, so I regularly say something is "about 4 ounces," and the same idea of something being "about 1000 feet" would likely be fine since you're already estimating.
You hit the nail on the head. Bases 12 amd 60 are much handier as they have more factors.
5040 is of course well-known as one of the most factorable numbers of all time:
2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520.
But 5280 isn't bad. And it gets 11, though it misses 7 and 9. 5040 only misses 11 out of 1-12.
5000 is pathetic. 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500.