If you stop pretending that universal time exists, then each timezone would need its own NTP stratum 0 atomic clock., Higher strata NTP servers would have to be told which timezone you wanted, and only return you the time sourced from whatever country's national labs count for that timezone, and those labs would not be allowed to compare each others times.

Each clock would run at a slightly different rate, based on imperfections in the equipment, the altitude of the laboratory and the amount of nearby mass in its vicinity. National clocks would drift, relative to each other, and so would everybody's timestamps. CET would be perhaps +1:00:00.000002 ahead of GMT rather than being exactly +1:00.

You'd have to continually measure and publish this drift in some kind of timezone-to-timezone comparison service, so that people who make network connections across the world don't end up finding that packets appear to arrive before they've been sent (due to National Clock drifts)

It's an interesting thought experiment. But I prefer where all the worlds' labs work together to produce a consensus universal time, and we just add fixed political offsets to it.

I like the odea of reference frames. But it isn't just geographic. The unix clock on a starlink is doing double digit mach and goes horizon to horizon in minutes. GPS satellites have always had to account for relativity, so we could look to that system... Hmm, seems gps time doesn't add leap seconds, only using those already added when it started ;)

Sure, you can define the reference frames to allow any orbit on any body. Mars landers & orbiters have slightly different time due to general & special relativity than Earth's surface, and also don't need Earth days/months/years, for example.