Another relatively common use case is version control systems. They rely, at least in party, on accurate time stamps to resolve check-out and -in conflicts. Especially if multiple developers are working across a WAN or in the cloud, those timestamps would be fairly important. And--I'm speculating outside my area of expertise-- wouldn't there be a serious security vulnerability with a time discrepancy on mission-critical systems? A way to insert malicious code in that gap?
So, yah, this is probably very important.
Do you have a single example of a version control system that uses time to handle conflicts? I have never seen a system doing that, they all just handle it by looking at which commit reached the server first.