Since the time we are talking about is going to be used by computers it might as well be base 2.
64 seconds per minute, 64 minutes per hour, 36 hours per day. You could then choose 8 days a week, 32 days per month, and 11 months (44 weeks) per year followed by 4.24... days of festivals to the pagan gods.
Just like before, the problem is that there are exogenous values: a non-constant length of year at an Earth location, a non-constant length of day at an Earth location, and a more constant period of time defined by a lower level process of nature like caesium atom vibrations for the seconds that scientists use.
I'm sure other fields do as well.
So go figure: which part of this system should be broken because people keep ignoring that leap seconds happen?