I think most people would look at the error and think "what's the big deal" but at all the telecoms customers would be scrambling to find a clock that hasn't fallen out of sync.
We actually disable NTP entirely (run it once per day or at boot) to avoid clocks jumping while recording data.
This doesn't seem right to me. NTP with default settings should be monotonic. So no jumps. If you disable it Linux enters 11-minute mode, IIRC, and that may not be monotonic.
But that’s all besides the point since most sane time sync clients (regardless of protocol) generally handle small deviations (i.e. normal cases) by speeding up or slowing down the system clock, not jumping it (forward or backward).
In our case the jumps where because we also have PTP disciplining the same system clock, when you have both PTP and NTP fighting over the same clock, you will see jumping with the default settings.
For us it was easier to just do a one time NTP sync at the beginning/boot, and then sync the robots local network with only PTP afterwards.
On Linux I think the adjtimex() system call does the equivalent https://manpages.ubuntu.com/manpages/trusty/man2/adjtimex.2....
It smears out time differences which is great for some situations and less ideal for others.
Worked really well for the project.
Avoiding time jumps was really worthwhile.
Perhaps a bit more boring than one might assume :).
There is a german club that builds and distrubutes such stations (using GPS for location and timing), with a quite impressive global coverage by now:
Synchronization is also required for SDH networks. Don't know if those are still used.
Someone else referenced low power ham radio modes like WSPR, which I also don't know much about, but I can imagine they have timeslots linked to UTC and require accuracy. Those modes have extremely low data rates and narrow bandwidths, requiring accurate synchronization. I don't know if they're designed to self-synchronize, or need an external reference.
When multiple transmitters are transmitting the same radio signal (e.g. TV) they might need to be synchronized to a certain phase relationship. Again, don't know much about it
It is very common to integrate a GPS in a WSPR beacon to discipline the transmit frequency, but with modest thermal management, very ordinary crystal oscillators have very nice stability.
We solved this by having GPS clocks at each tower as well as having the app servers NTP with each other. The latter burned me once due to some very dumb ARP stuff, but that's a story for another day.
Precision Time Protocol gets you sub-microsecond.
Timekeeping starts to become really hard, often requiring specialized hardware and protocols.
edit: also the linked slides in TFA
Distributed sonar, allows placing receivers willy-nilly and aligning the samples later.
Remote microphone switching - though for this you wouldn't notice 5us jitter, it's just that the system we designed happened to have granularity that good.