Do we care what time it is?
Do you have a control system that only uses buttons and lights to interact with operators? Is it missing real-time trending, alarm historian and regulatory reporting? There are certainly control systems that don't have a need for accurate clocks, but they are few and far between. Let us assume you do not have one of those systems and keeping time is vital to your operations.
It is always good to have accurate time, but it is more important to have synchronized time. If every clock in the building is 10 minutes slow, then you can still tell which of two events happened first. You're going to have a big problem on your hands if your DCS has one time, your database server has another, a PLC has a third, and they all drift independently. Sequence of Events (SOE) operations, time stamped I/O and alarming, and synchronized motion are all applications that mandate synchronized clocks.