The only one I can think of is: determining the phase of the 24 hour day (as measured by atomic clocks) with respect to the Earth's rotation.
It does seem logical use TAI for civil time. People interested in calculating the Earth's rotation to high precision could consult a regularly-updated publication somewhere.
Eventually the Earth's rotation will drift out-of-sync with the atomic clock timebase, but that won't be important until we accumulate several minutes/hours of error from TAI which could be centuries from now.
Unfortunately, electronic devices come with quartz crystal resonators, or rubidium or cesium resonators. After frequency calibration these will keep stable time relative to the atomic clock timebase.
There is no device available that allow you to derive a clock from the relative motion of the sun about the Earth’s axis, such that the changing definition of days and seconds relative to realizable clocks can be tracked.
Furthermore it’s kind of nice to have a stable and standard definition of seconds and days. For instance, under the “ut1 system” you don’t know how long a present second is until the present day’s final observations are made.
It does seem logical use TAI for civil time. People interested in calculating the Earth's rotation to high precision could consult a regularly-updated publication somewhere. Eventually the Earth's rotation will drift out-of-sync with the atomic clock timebase, but that won't be important until we accumulate several minutes/hours of error from TAI which could be centuries from now.