My former Props Master used to set up a digital clock backstage right on his prop table (since he always worked on right), and he would set it himself with the downbeat. After he left, no one else did this. As Maribeth said, most of my current crew either set a stopwatch or use the stopwatch setting on their phones or wrist watches.
I think the problem with a fixed clock is that it's only in one place - so only one side of the stage sees it, and depending on where it is located on that side, even fewer people may be able to see it. Just easier for crew members to take care of themselves, or ask a member of Stage Management how long until the next cue.