There's "Google time", their approach to leap seconds. 12 hours before a leap second, Google's version of UTC time starts running slightly slow, so that it loses a second over the next 24 hours.[1]
Some Google database systems rely on tight time synchronization to order update events, so they had to have a global monotonic clock.
Dealing with time well into the future is rough because of the unknown timezone changes and unknown leap seconds. There's not much you can do.
Computing future times in TAI from user inputs in wall clock time is fraught, so I guess you can't store TAI in those cases.
For a calendar app, since users want to deal in wall clock time, you have to store time with timezone and with leap seconds (so UTC + time zone). And you have to store timezone, not offset to UTC -- timezones can change.
At least internally, however, dealing in TAI can be helpful[0].
Also, IIRC there's a proposal to redefine UTC as without leap seconds[1]... That scares me. Users really need wall clock time.
The continued existence of TAI was questioned in a 2007 letter from the BIPM to the ITU-R which stated "In the case of a redefinition of UTC without leap seconds, the CCTF would consider discussing the possibility of suppressing TAI, as it would remain parallel to the continuous UTC."[16]
"That scares me. Users really need wall clock time."
Why would getting rid of leap seconds from UTC be a problem for that?
The reason there are leap seconds is nothing to do with wall clock time, it's because some people feel the time ought to be intimately connected to the Earth's rotation, but the Earth doesn't oblige by rotating steadily.
In my view the people demanding this relationship be maintained ought to take responsibility for fixing it from their side. Speed up or slow down the Earth. Can't? Too bad then, but don't expect us to keep fiddling with the clocks.
Wall clocks just track UTC. Today they have leap seconds because we defined UTC to include leap seconds, tomorrow if UTC or a replacement universal time no longer has leap seconds then wall clocks won't have leap seconds.
You are probably thinking of sun transit time, "solar noon", the moment in each day when the sun appears to be "highest" in the sky. This varies of course by position on the Earth, it's how people set "noon" when they didn't need to agree with anybody more than a horse ride's distance away what the time was. So, let's say at least 200 years or more ago.
Do you know when solar noon is where you live now? No? Because it's irrelevant. Huge numbers of people live in places where the solar noon changes by an entire hour twice a year for no sensible reason. Does this cause a huge problem? No, there's a slightly elevated rate of road accidents and things like that, but nothing major. A few seconds per decade is _nothing_.
For example, if you store time in TAI then you'll have to recompute all other future times as leap seconds are announced.