Local time zones are offset from UTC, not TAI. If it's 19:45:00 in LA, UTC is 02:45:00 and TAI is 02:45:35. There's no such thing as a "TAI version" of your local time.
The solution is simple math, for computers to base their time on TAI, the time zone conversion changes from "UTC + local timezone offset", to "TAI + UTC offset + local timezone offset" and we reap the rewards of drastically simpler software at the core of our systems.
TAI is defined like UNIX time, as a notation of the progression of proper time. It is the primary reference by which we build all other times, UTC is a humanist overlay on TAI to maintain norms, since we need an approximate terrestrial solar time for sanity purposes.
If the math changes to TAI as the "base storage representation" for time stamps and reference time internally, then the math becomes immediately sane, since TAI can be relied on as a direct sequence of mathematically related linear time without lookup tables or other crap. Move the crap "up the stack" to where it doesn't cause issues like these we see every time things need a leap second.
The problem is that "the system clock" in the sense we have it now is actually "overloaded" with different expectations. From the hardware point of view, we have hugely inaccurate timers on the motherboards possibly drifting a lot all the time.
Then we have the signal from GPS, but typically only on the mobile phones, and some other signals on some other distribution mechanisms:
"GPS time was zero at 0h 6-Jan-1980 and since it is not perturbed by leap seconds GPS is now ahead of UTC by 16 seconds.
Loran-C, Long Range Navigation time. (..) zero at 0h 1-Jan-1958 and since it is not perturbed by leap seconds it is now ahead of UTC by 25 seconds.
TAI, Temps Atomique International (...) is currently ahead of UTC by 35 seconds. TAI is always ahead of GPS by 19 seconds. "
And we have NTP servers, which differ from one another all the time, and to which our computers connect and try to adjust what they report.
So the bugs are already just in how the adjustments are handled, not that the world can be made simpler.
Q: What value of TAI will be noon of July 4th, 2030 in New York?
A: Honestly, nobody knows.
You can estimate the number of leap seconds, but not know (much) in advance. Having (future) date representation chance occasionally does not lead to sanity either.
