You're asking about time standards. In this area, it's important to understand context about how the standard is intended to be used.
Taking your question directly, the time standard you're describing is International Atomic Time (TAI). It is the standard that all of the world's timekeeping institutions (NIST, NPL, etc.) use to coordinate their clocks. It is super useful for this purpose, as this is what it was designed for. It does not have leap seconds.
However, TAI is rarely used directly in computing or business. The only time standard that matters for most of us is Coordinated Universal Time (UTC). This is what your computer's system time tracks, and we typically synchronize to this standard using NTP. It does have leap seconds.
The PTP protocol can be used to synchronize a computer's clock to either TAI or UTC. This is because TAI is the basis, but the protocol separately carries the current offset between UTC and TAI.
Most systems don't display leap seconds. Instead, they are typically absorbed during synchronization. In other words, after a leap second occurs, a system might deviate from UTC by one second until its next synchronization. However, this behavior can vary across systems and platforms. Some may choose to display it directly. Some may "smear" out the leap second across the day.
Unix Timestamps are interesting in that they both do and do not have leap seconds, depending on how you interpret the problem. They do have leap seconds in that the timestamp is aligned to UTC, so any timestamp you interpret is inclusive of all the leap seconds that occurred to date. But they don't have leap seconds in that there is no accounting for them in the calculation. The calculation is an exact number of seconds since the Unix epoch (1970-01-01T00:00:00Z
). In other words, the Unix timestamp of a leap second itself (such as 2016-12-31T23:59:60Z
) is ambiguous.
Ultimately, in day-to-day computing, you probably shouldn't choose a standard other than UTC or be concerned about ambiguity of Unix Timestamp leap seconds unless you have very specific use cases where leap seconds become an issue.