Out of curiosity, can anyone say the most impactful things they've needed incredibly accurate time for?

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.

Spanner

(See https://docs.cloud.google.com/spanner/docs/true-time-externa...)

Spacecraft state vectors.

Telling people at the bar that I have an atomic clock at home.

Not sure but synthetic massive aperture radio telescope would need syncing their local clocks.

I defer to the experts.

GPS