Out of curiosity, can anyone say the most impactful things they've needed incredibly accurate time for?
Telling people at the bar that I have an atomic clock at home.
Spacecraft state vectors.
Not sure but synthetic massive aperture radio telescope would need syncing their local clocks.
I defer to the experts.
GPS
I work at a particle accelerator. We use White Rabbit (https://white-rabbit.web.cern.ch/) to synchronize some very sensitive devices, mostly the RF power systems and related data acquisition systems, down to nanosecond accuracy.