Blank days
The tropical year is a bit longer than 365 days. Coincidentally 364 (with its prime factors 2, 2, 7, 13) is divisible by seven, the length of a week and also by four, to get quarters. Many calendar proposals (including SAC13) are built around that 364 day year, because it allows for especially simple and pretty calendar layouts. But a year is longer than 364 days, so unless we want the calendar to drift a lot, we have to somehow cram in a day (or two on leap years) but without ruining too much of the pretty layout we got by designing around 364 days.
Some calendar proposals (e.g., International Fixed Calendar, Positivist calendar, World Calendar) try to fix that by defining those intercalated days to be outside of any month and week with no ordinal number. At a quick glance it might look like a good idea, because defining them outside of weeks and months allows the rest of the calendar to be extra pretty because there is never a 29th of anything. Some proponents of such calendars even claim that they don’t break the week cycle because those days are outside of weeks.
But if you think about it, it’s not a good idea at all. It’s like
children “cleaning up” their room by sweeping everything under the
bed and then defining “under the bed” as somehow outside of the
room. It’s also bad because, between the years those calendars were
proposed and today, computers happened. It would be a nightmare of
edge cases to define those days outside of months and weeks, and
without ordinal numbers. What would the calendar on your smartphone
look like on or around that day? It’s not impossible but it’s
impractical and unnecessarily complicated. What would an
ISO-8601-like date format look like for that day?
2000-06-27, 2000-06-28,
2000-LeapDay, 2000-07-01? How would an
accountant type that on their Numpad? It would also be completely
undefined which period to attribute stuff to, that happens on a Leap
Day or Year Day. If you use electricity on that day, is that billed
in the previous month or the next month? Or do you get a separate
bill just for Leap Days? So, in practice the Leap Day and Year Day
will always be considered part of a week or month, but if the
calendar system defines them to be somehow outside of weeks and
months, everybody will just start doing their own thing (like using
2000-06-29 or 2000-07-00 instead of
2000-LeapDay) and the mess would be perfect.
SAC13 takes a more honest approach. The reason why we have those sync days is because we want to sync up the calendar with reality, and to make sure everybody agrees on where to attribute stuff to that happens on sync days. They have a clearly defined week, month, and ordinal number. Of course it’s still an edge case, but a fairly trivial one and most importantly: There is no ambiguity and everybody agrees on how to handle it.