Perhaps its police who aren't in stations who need to have the EXACT time because it needs to be recorded for evidencial purposes.
For instance, say if an officer arrests someone and records the time of arrest at 17:05 by looking at their wristwatch that then turns out to be running five minutes fast.
In court, the defence could launch into:
"How could the accused have possibly gone from point a to point b in less than two minutes? It's physically impossible even for an Olympic sprinter!"
Case dismissed, tax-payer's money wasted, scrote back out on the street.
Possible?