I wonder if there's things that run 24/7 and need to be monitored.. e.g. if you have oil flowing through some pipeline at 100 liters/second, one particular minute will have 6100 liters, and someone will want to get paid for that 100 extra liters.

But the meter/reporting tool would say "Well, we measure every second, and the meter reported a constant rate of 100 liter/second, and as we know we have 60 seconds in a minute, so we got 6000 liters!".

Or a database for "measurements every second for this minute" that has 60 fields, and don't have a field for the 61st measurement.

Systems definitely care, especially in finance and trading systems.

Was involved in rolling out a large NTP annealing patch about ten years ago. We missed a couple and the effect was largely overall muted, but we did have one server with an old JVM hard crashing the server right at the second shift.

That specific server was already hobbling along so it wasn't a surprise. But it required a bit of firefighting.

The problem frequently crops up in order-deterministic systems that use time and haven't accounted for the edge case of all the vagaries related to time-keeping of this being only one.

I've worked on some extremely sensitive systems that had thousands of lines of C dedicated to handling skewing a time gap across an hour-per-second when necessary. I know that code assumed only "missing" time (jump-forwards)... Even knowing what I know as a developer now, if I was re-implementing that system from scratch and didn't have this top-of-mind, I'd bet I would miss "overlapping" or "duplicate" time entirely.

Maybe that is more of a me problem than others, but I'd bet there are some safety critical systems out there where the responsible engineers, QA, and specs all missed this as well.

GPS uses its own time base that doesn't do leap seconds. For display purposes, the leap second offset to UTC is transmitted to the receivers and added to the displayed time if needed.

traditional markets are closed when time changes happen