and a computer will probably do it for them automatically, and a lot of people won't even have to worry about it at all during their lifetime
Which is why I raised doubts that a computer would be programmed to do it correctly to begin with (it will only be on the minds of programmers near that 128-year threshold), and doubts that it would be remembered at all ("Just let the machine do it").
Each... quarter are of constant length
Of dubious value, as tropical seasons are not of equal (or uniform) length, and the beginning and ending dates of your quarters will be non-obvious.
Each time measurement unit begins at 0
Every single law and contract mentioning "the first of the month" will need to be rewritten to be unambiguous, since "1st day of the month" and "day 1" will be two different days.
Each quarter lasts for 3¼ months or 13 weeks
Only if you ignore your epagomenal days. Food and fuel must still be consumed, rent must still be paid, and interest must still be accrued. Your perpetual quarters are actually 91.310 546 875 days exactly.
This brings us to the general problem of epagomenal days to begin with: for trade and commerce, are they to be treated as being part of the 1st week/month/quarter (not to be confused with "week/month/quarter 1") or the last? And if that question can and will be answered for all purposes, why insist on epagomenal days to begin with instead of explicitly appending them to the prior or following week/month/quarter? Leaving them epagomenal will only breed ambiguity, which will breed lawsuits.
Note that, in the current system, bissextile days are explicitly part of February and additive leap seconds are explicitly part of 23:59 UTC.
Calendrical drift is suspended by including leap days in years that are a multiple of 4 but not of 128
There is no such thing as a perpetual calendar. Comparisons between algorithms of intercalary days can only be valid for about one millennium from now. Even the current standard of leap seconds itself (which allows for up to 12 adjustments per year) will break down around then.
All written dates are unambiguous.
But the relationship between cardinal and ordinal dates will become ambiguous.
zero-basing: Most standards (like ISO 8601, UTC, TAI) today define 00:00:00 to be the equivalent of midnight and therefore occuring on the next day
Not everyone within industry is compliant with those standards (I again raise the example of POSIX). You're presuming that, along with your calendar itself, not only all of industry will finally properly adopt and abide by these standards, but the general populace as well.
Consider that the general populace can't even agree on the starting point of a new day for all purposes. As an example, meteorology generally treats dawn/sunrise as the beginning of a new date, as demonstrated by the timing of low temperatures predicted for a particular date.
I had a middle school substitute teacher back in the day that told me that midnight occurs on neither side, but simply in between the two, so, technically, it's in neither day.
Your substitute teacher was expressing a personal opinion, one of several. And we haven't even gotten into the definition of midnight itself.