One of the biggest problems is that weekdays completely cease to make sense. With timezones, the day of the week changes at midnight, when most people are asleep. You wake up in the morning, it's a new weekday, and it's the same weekday for as long as the sun is in the sky.
If we abolish timezones and choose UTC as the one time, the day of the week will change at 5pm in San Francisco. Say that you have an establishment that is normally closed on Sundays. It's 4pm on a Saturday, do you close in an hour because it is then Sunday? Or do you change your "schedule" so that your establishment is closed on SundayMondays instead? Or perhaps you keep it closed on SaturdaySundays? Because the concept of "Sunday" doesn't make sense anymore, "Sunday" is no longer a contiguous period of normal waking hours.
In San Francisco. In London it's business as usual. But in Sydney the day of the week changes at 10am. When is "Sunday morning"? 9am Sunday morning is the day after 10am Sunday morning. Every week has two Sunday mornings now. (And two Monday mornings!) Which one of them did you mean?
Adjusting computer systems is much, much simpler than getting humans to accept this idiotic system.
Agreed -- I think of timezones much like coordinate systems: They're all representing the same point in (space|time), just in a slightly different format, each with different benefits/setbacks for biological things vs electronical things. Like latitudes and longitudes vs UTM coordinates vs local grid coordinates. "Number of milliseconds since January 1st 1970" can still describe the same global time-point as "First of July, 2019, noon". Timezones are there for people. Everything else can normalize on UTC.
That being said, I think the "universal" in coordinated universal time is a bit of a misnomer -- at some point in our interstellar future, are we going to have to start thinking more about factoring in time dilation? :-) we already have "coordinated Mars time".. Are we going to have an intergalactic day of many noons..
If anything, it's the computers that would have the easiest time of things. Time is already so random and janky that on the whole the computing world has dealt with it reasonably well. It would "just" mean one more entry for every timezone in the Olson timezone DB, and that's a lot of the work right there.
However, by the same token, if you want to get a sense of just how impossible this is going to be to get anyone to agree to from the political side, a read through the comments in the timezone DB can be constructive, such as: https://github.com/eggert/tz/blob/master/europe
It'll really show you what anyone who thinks they can convince the whole world to change is up against.
Except for the literal billions of computers which will need replacing and trillions of lines of code you're going to need to rewrite, sure.
And redeploy the entire GPS system. And the code running on the mainframe in the back room of the basement which no one has touched in literal decades.
Seems.... Risky