Bah. Just use POSIX time. To Hell with 12-hour clocks, 24-hour clocks, DST, leap seconds, time zones, minutes, hours, days, etc. Just one number that is what time it is, increments by 1 every second, and will keep doing so at that rate forever. Simple, easy, unambiguous, and totally unrelated to arbitrary astronomical phenomena and all the complexity they add; if for some reason you care where the Sun is, you can just do the modular arithmetic to figure it out.
The main problem is that working hours and people's lives are still synced to local solar days.
One problem with everyone using universal time is best explained by example.
Currently, you call your uncle, who lives elsewhere. He says "why are you calling now, it's 3AM". You immediately know you called at a bad time
without having to do any math. It's 3AM where he is, and that's unambiguous. Also, you don't have to know the time offset from where you are to where he is to know what that means. Call later.
However, let's call your uncle after we've abolished time zones. Now, he says "why are you calling now, its 1100GMT!" without knowing his location, you have no idea what that actually means in terms of waking hours at his location, so the guy needs to append some sort of "solar offset code" to the time information so that you know what actual time it is at his location, defeating the purpose of removing time zones.
If it's necessary to coordinate across time zones, just use GMT time. If you're one of the
very rare people who needs to know the raw number of seconds then you can easily get that information. There's no reason to upend everyone's lives to accommodate such an obscure need.