This is actually what the Precision Time Protocol (PTP) does. It's the successor to NTP, so it improves on some of NTP's mistakes. The protocol uses TAI, but also sends the TAI-UTC offset so the computer can display times in UTC.
But that's backwards. A Stratum 1 NTP usually gets its data from GPS, which HAS the offset (GPS runs TAI). But it only outputs UTC, but not the offset, making other programs compute it from TZDATA. Why is NTP making user programs harder to get the data that IT ALREADY HAS? Because philosophically, NTP is married to UTC (even though NTP is mostly for computers!)
And providing this offset would basically get rid of a large body of people (like the TFA) who wants to CHANGE the definition of UTC, which is a more drastic proposal.
GPS time is actually 19 seconds behind TAI at all times.
1. Displaying current time: for that ideally you need the offset directly from the time server because the system timezone data can be out of date in regards to current time.
2. Displaying historical timestamps: for that you use the system timezone file.