The most obvious uses for a local time server are when the network can't get a connection to the Internet, or the connection is unreliable and you absolutely need accurate (or at least, consistent) time.
Other than that most people sync to an internet NTP provider, but this leaves you open to problems with that provider's service, for example the recent issues with the US Naval Observatory's NTP service having issues causing some people's networks to "time travel".
One way to get around that is to run your own time server. While it's still liable to be affected by the occasional fault, at least you can (hopefully) monitor it yourself to catch any issues that might affect the time its issuing and you can certainly control how issues are resolved to mitigate any problems this might cause.
In an ideal world you'd be using multiple time sources to try and ensure accurate time that couldn't be ruined by one source going down.