For example, deleting your entire codebase and firing all your developers is painful, but even the most continuous deliverer wouldn't advise you to do that more often.
Getting past pedantry, the advice is obviously about foreseeable, repeating parts of normal business, and it applies to more than devops.
A long time ago (tail end of the "desktop publishing revolution"), I was a production assistant, and then manager at a magazine. We published six times a year. Towards the end of my first year there, I realized we had the same problems, right down to our Advertising Director's emotional meltdown, every. single. issue.
After getting to know folks working at other magazines and people at our press, I noticed that the monthlies seemed to run smoother with less drama, and the weeklies were even better at it. Eventually I realized it was because they had to be. If there was some minimum amount of human drama that had to happen, it was forced into exhibitions that didn't disrupt the (tight) schedules. If last-minute changes from flakey advertisers came in, they didn't cause a firedrill, they just didn't run, because that issue is already on the press and we're talking about the issue after next now. And so on.
The general principle is actually very straightforward, and applicable all over the place, including your personal life. If you have high-friction processes, devoting time and attention to them is the way you make them lower-friction processes. And while it may be possible to do that without doing things over and over until you get there, it probably is not possible for you to get there without repetition, else you'd not have the problem in the first place.
That is what a lot of organizations do, "smearing" the leap second since they know their systems can't handle the discontinuity. I think this shows that software has failed in general at handling leap seconds correctly. As another said, I think leap seconds are unnecessary complexity with the frequency at which they happen.
That only works assuming you need to do it at all.
If leap seconds are useless (to the majority of users) or insufficient, not doing them is preferable to doing them constantly.
The best solution is probably just to use a nice number of seconds per day and accept the fact that in 100ish years summer will start in March, not December. It's not like we need to build our entire society around planting and harvest any more.
Not to mention with climate change, we're probably going to have to deal with many other changes in season etc. anyway.
All of us deal with the fact that the day gets shorter and longer every year anyway (and daylight savings didn't seem to be a terribly good solution).
I think having the seasons slowly drift is a non-issue, provided it's just slow enough to not be noticeable from year to year.
Of course, once you start dealing with astronomical distances and speeds, the whole concept of a single universal measure of time kind of goes out the window anyway so it's probably going to get worse, not better. :P
(FWIW my definition of 'best' here is something along the lines of 'simple, no special rules or tinkering, gets translated to a human-readable local time on demand'. Which is pretty much how Unix epoch works, come to think of it.)
So, if leapseconds are actually painful for you, then maybe we need to contemplate making this kind of adjustment on a finer timescale, like milliseconds.
OTOH, if you think leapseconds are painful now, just you wait until you postpone this pain and do it even less frequently.