Also 0.0001% of the distance to a GPS satellite is on the order of 200m. Not impossible to work with, but not great either. Though I have no idea what the exact ramifications would be.
https://www.gps.gov/technical/icwg/IS-GPS-200K.pdf
* recent satellites have limited autonomous navigation capability as a backup.
Just like you can convert between UTC, TAI and UT1.
I don't follow. Outside of days with a leap second, you are using the SI second.
If you're measuring skew via raw-seconds-since-epoch or something similar, that's already an error-prone measurement. It's a non-goal for smeared UTC to be synchronized with TAI, just as it's a non-goal for unsmeared UTC to be synchronized with TAI.
It's internally consistent, and for communicating with external entities that expect unsmeared UTC you convert as needed as much as possible. No different from if you were running TAI and communicating with unsmeared UTC, or communicating with TAI while running unsmeared UTC.