That's mainly a holdover from mechanical clocks - a lot of things were based on gear wheels with 60 teeth, or multiples of 60. 365 days is kinda imposed by nature.OTOH, quite a few Standard measurements work well for those who have little math ability. Unlike base 10, 12 inches can be divided evenly in several different ways, as can 36 inches. 5280 can be divided in a truly astounding number of ways, including by 11 (but not 7 for some reason). Yes, they are a holdover from a less advanced time, but so is almost everything everything else you can think of.
Nice idea, but not true, mechanical clocks had gears with 60 teeth because time was divided in units of 60, not the other way around.
Check this wikipedia article:
Wiki on 60 seconds/minutes.Wiki: Unlike most other numeral systems, sexagesimal is not used so much nowadays as a means of general computation or logic, but is used in measuring angles, geographic coordinates, and time.
One hour of time is divided into 60 minutes, and one minute is divided into 60 seconds. Thus, a measurement of time such as "3:23:17" (three hours, 23 minutes, and 17 seconds) can be interpreted as a sexagesimal number, meaning 3×602+23×601+17×600 seconds or equivalently 3×600+23×60−1+17×60−2 hours. As with the ancient Babylonian sexagesimal system, however, each of the three sexagesimal digits in this number (3, 23, and 17) are written using the decimal system.
Similarly, the fundamental unit of angular measure is the degree, of which there are 360 in a circle. There are 60 minutes of arc in a degree, and 60 seconds of arc in a minute.
In the Chinese calendar, a sexagenary cycle is commonly used, in which days or years are named by positions in a sequence of ten stems and in another sequence of 12 branches; the same stem and branch repeat every 60 steps through this cycle.
Why exactly there are 24 hours in a day has something to do with the duodecimal system the sumerians also used, but exactly what, I don't know and can't seem to find any convincing reasoning on...
365,24... days a year is pretty obvious, making that 100 days or 1000 days a year simply isn't practical...
Edit: fixed link.