Few people or systems even interact with a clock that is precise enough to detect the difference, and instead rely on clocks that are 100's or even 1000's of times less accurate than what would be required to even detect a leap second. And these clocks undergo thousands of corrections between leap seconds without a complaint.
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.
Leap seconds are needed in civil time because people's schedules are still dominated by the Sun. Not to the second, maybe not even to the hour. But the leap second was chosen because it's large enough to be infrequent, and tiny enough that only a tiny fraction of systems will notice.