I don’t see how dealing with that is any worse than dealing with time zones.
Downside of UTC everywhere: you might have to set your alarm for a different time when you travel.
Upsides: Never need to account for timezones in communication. Never need to change a clock, ever.
They make sense because the numbers won’t be arbitrary.
But they are. There’s no changing that. They’re arbitrary now. They’d be arbitrary if we had UTC everywhere. We’re not out here using sundials to set our clocks, 12:00 is not solar noon more often than it is.
It definitely would not be, regardless of whatever “done correctly” means. Solar noon at exactly 12:00 is only going to happen on a single line of longitude. If you have a timezone centered on that line and exactly 15° (one hour) wide then solar noon will be up to 30 minutes away from 12:00 depending on your east/west position in that timezone.
It was exactly this realization that the numbers were arbitrary and 12:00 didn’t need to be solar noon that led to the creation of timezones in the first place, so that it’s not 4:14 in Norwich while it’s 3:52 in Birmingham and just travelling from city to city doesn’t mean you’re changing your watch constantly and it becomes actually possible to write a sensible rail schedule.
Timezones are already a step toward an arbitrary standard time for the purposes of making communication easier and not needing to change your watch just because you moved around. UTC everywhere would just be another larger step in that already established direction.