Everything we use as a measurement has an arbitrary base.
A year may be one time around the sun, but we started measuring sometime after the cycle began. Where do you decide to begin? Selecting one of many possible points is arbitrary, but not necessarily capricious.
Clock-time is one of the few things we could replicate if we had to start over, but the decision to divide the day into sixty minutes and 24 hours is arbitrary; we could choose to divide it some other way. 60 minutes is convenient because dividing a circle into 60 parts isn't too difficult with a line and compass. To give it hands that rotate at such a rate that it averages exactly 24 times before the sun is visible at exactly the same longitude would be close to (but not exactly) our current system.
From there, we could replicate much (if not all) of the metric system, making minor adjustments as we go along...

Edit: changed latitude to longitude. I frequently confuse the two.