I think the article and much of the discussion misses a larger point -- time is hard, and very very hard when there are multiple systems with different clocks. The APIs are the way they are because there just aren't solutions especially since all systems ultimately have unreliable connections to good time sources.
The miserable APIs are New Jersey/Worse-is-better answers to intractable problems.
Basically, my takeaway from this is: if you /can/ avoid the complexity, by dealing with absolute relative timings (if something takes 2 seconds, then it takes 2 seconds, even if one of them is a leap-second), then you /should/.
And the best way to do this is using the techniques mentioned in the article
The miserable APIs are New Jersey/Worse-is-better answers to intractable problems.