The problem with TAI is that the rest of the world uses UTC. So you can use TAI on a small island and then you have to convert to and from UTC. My hobby kernel is based on TAI internally. And it constantly converts to and from UTC.
You do not use TAI to communicate with the rest of the world, except for certain special purposes.
As you say, what the computer should maintain internally and for communication with other computers, not with humans, is only true time and not other quantities, like the angles between Earth, Sun and stars.
Only TAI is true time, while "universal time" is an angle and "universal time coordinated" (UTC) and its derivatives are some weird hybrid quantities that can be computed from times and angles.
The conversions between true time and various kinds of official times used by humans are very complex and they should be handled in a single place, not in various places that may handle time zones and discrepancies between UTC and TAI and various other "times", e.g. UT2, UT1 etc.
