Any time you show the time to a user, you have to use a timezone. That's why the unix timestamp has limited usefulness - it doesn't do a lot on its own and practically all use cases for times require the timezone to be known (unless you're dealing with a system that can both store and display dates in UTC). Even for things like "add one week to this timestamp", you can't do that without being timezone-aware, since it's not always an exact number of seconds as you need to take Daylight Saving transitions and leap seconds into account.

Then that system should be trashed.

A lot of systems just don't handle leap seconds well. Many years ago, Reddit was down for four hours because their systems couldn't deal with leap seconds. Smearing the extra second across the whole day causes fewer issues as software doesn't have to be built to handle an extra second in the day.