60 is indeed handy since it divides into 2, 3, 4, 5, and 6. 30 would be much less convenient. Better to drop the 5 (as evidenced by 12 and 24)

I think the gp just generalized a bit to much. Units of time weren't chosen for those (prime) factors. People had simply figured out long time ago that a dozen is a nice round number.