So no, as a human being, I'm fine with base 10.
If you don't make the base of the number system agree with the base used for converting between units, then conversion becomes so much harder. For example, it's not immediately apparent that 204 inches is 17 feet, but it is immediately apparent that 204 cm is 2.04 m. Furthermore, when the base disagrees with conversion factors, you run into issues like variable-length fields - like, "2ft 9in", "2ft 10in" (notice the inches transitions from one digit to two digits).
A true base-60 would have 60 unique symbols for the different digital values, much like how in our set of ten digits {0123456789}, none of the symbols have any rhyme or pattern with respect to the others.
Good luck memorizing the ~1800 entries of the base-60 multiplication table.
Base 10 really is used because our number system is base 10. And more so base 1000. Apart from some cultures.
As for changing the world to counting in base 12, yes there would be some advantages, but really, good luck with that.
Let’s go hexadecimal all the way.
Switching from Base 10 to Base 12 would be difficult. Instead we should go back in time and ensure we evolve with 6 fingers on each hand and foot.
https://www.wikihow.com/Multiply-With-Your-Hands
Those techniques can be useful. If you add toes, multiplying numbers up to 20 (like 16x18) is easy.