> Does anyone have an actual example where leap seconds are a problem? Specifically one that can't be solved simply by using Atomic Time? Maybe then we can figure out what the problem we're trying to solve is.

Any time that is supposed to represent both a wall-clock time has to deal with it.

There is currently no known answer to the question "What is the interval between the unix time stamps @1720026000 and @182002600" However, there is a well defined answer to "What is the UTC time for @182002600" and thus also "what is the local time in a timezone with UTC offset X for @182002600"

If we were to redefine Unix time to use Atomic Time, then we could answer the first question but not the second.

> We add an entire day to the calendar about every 4 years. It's not a problem because everyone is aware of it. So I think the only real thing that needs to change about leap seconds is awareness of them.

It's not just "about every 4 years" it's precisely "every 4 years, except for centuries, except for quad-centuries." If you give me any year, I can tell you if it will be a leap year. I can program a non-internet connected device and it will get leap years right indefinitely. Leap seconds are not predictable, but rather determined empirically and announced about 6 months ahead of time. Any device that wants to properly account for them needs to be updated at least every 6 months to be correct.