It's like you buy a cat to help with your rodent problem, figuring the cat will eat mice and isn't much trouble to look after, but after purchasing a cat you find that your problem was actually rats, your cat is terrified of these large dangerous creatures and sometimes gets bitten by them necessitating expensive vet bills and now you need to pay a lot of attention to the poor animal and also now need to buy cat food.
I mean we deal with daylight saving time all the time and I know it's not the same because the leap second affects UTC, not just local time zone, it's just that you are either dealing with monotonically increasing time like epoch, or you are dealing with "human" time and I found no distinction in the latter.
Is it "just" that leap seconds or delay seconds caused problems in epoch to utc conversion? Note the just in quotes, but did I just answer my own question? :)
Those things that really do rely on actual "elapsed time" rather than the difference between two recorded "book times".
Does this happen? Yes, a few times in my career in geophysical exploration - it's why multiple bits of gear are synced to a reference "real clock" which gets logged against the raw GPS epoch time (real time since Sunday last week(?)) and processed "UTC" time (some variation of it).
There's a lot of fiddly pedantic stuff that goes with scientific data recording, timekeeping is but one domain of possible issues.
And I wish we didn't every year!
We also don't deal with DST very well either. You won't believe the amount of programs written that treat local time as monotonic. It causes all kinds of problems and most people roll their eyes when someone who knows pipes up about local time and time zones etc.
If the world weren't entirely reliant on software to the extent it is today (like when leap seconds were introduced in the 70s), it wouldn't matter as much.