The practice of dividing the degree used to measure angle into sixty minutes of arc, and that into sixty seconds of arc is over 2000 years old. The corresponding practice of dividing the hour used to measure time into sixty minutes, and that into sixty seconds, is over 1000 years old. Why sixty? That's over 5000 years old. The Sumerians and Babylonians used base 60 arithmetic.
Old practices die hard. In the case of angle and time, they haven't died yet. The French metric system promulgated in the late 18th century worked fantastically for mass and length (and related concepts such as area and volume). One key factor in this success is that there were no standards for mass, length, area, and volume.
The French also tried to metricize angle and time; there they failed. Old practices die hard, particularly when they are very well standardized. We still use degrees, minutes, and seconds to describe angle, and hours, minutes, and seconds used to describe time. Given that there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute means there are 86400 seconds in a day.
The success of the meter and kilogram and the failure of decimal angle and decimal time taught early metrologists something. When no standard exists, make one up. When a standard does exist, it's best to follow it. Now that we have well established standards for everything that is physically measurable, meteorologists follow the second rule. Redefinitions of a standard are always consistent with previous definitions. For example, the definition of the meter has changed multiple times. The current definition appearing to be completely arbitrary. It's not arbitrary. It's consistent with the initial definition of the meter.
The same goes for time. While the definition of a second has been refined many times, it has always been done in a manner that is consistent with the thousand year old concept that a second is 1/86400th of a day.