Right now, you understand the basic meaning of different times no matter where you are: Noon means lunchtime, 8am is rather early, 10pm rather late etc. You can travel and this doesn't change. You can watch British movies and you'll understand the time references.
Switching to UTC changes all that. And, almost as important, it doesn't help in the least: you still need to think about your co-worker's geographic location when trying to find a time that's good for your phone call.
It sounds like a decent idea on the surface but then times would be meaningless. Right now a time "means" the same thing everywhere. When we ask "what time is it in Japan?" we understand the answer. We understand when its "noon" in Japan, we know whereabouts in the day it is and what we can expect people to normally be doing, ex, eating lunch. If it's 3am in Japan we know its not a great time to call beyond emergencies.
If you're in the East Coast US and its 5am and at the same time its also 5am in Japan, but they mean different things, you no longer "understand" what time it is in Japan. You don't really have much of a way of answering "is it a good time to call someone in Japan?" - You have to figure out a way to "translate" from your time to theirs. It would be very, very confusing. So in the end you'd end up re-inventing time zones.
It only works if nobody knows anything about other parts of the world.
An alternative is just to count seconds. Be as precise as you need (m? k? M?). A little like unix timestamps, except without the rule that says "there's 86400 of them in a day no matter how many seconds there were in that day".
And then let "Sunday", "Monday" etc become simply approximate terms. And I never have any idea what day of the month it is so I don't care. (Birthdays and public holidays are set based some recurring feature of the count.)
A refinement of this uses a time period that is approximately 100,000th of a day so then people can easily notice the day. In practice we might use hectokiloperiods instead of periods. Someone will invite a less woeful name.
Nothing about telling time will be particular familiar. Doesn't mean it won't work. But I suspect it'll be awful. I'm fine with daylight savings and all the rest of it. Except days of months. Can't we just say "Monday, third week of June"? or "Wednesday, 39th week"?
Except, instead of converting your time to theirs and thinking "oh, that's too late for them". You have to come up with some other conversion. Hmm, it's 9pm for me on the west coast, so 9pm is 9pm late or early for NYC? What is a normal bed time in NYC?
We would basically be replacing standard timezone conversion with some kind of non numeric system of identifying the time of day in a place by comparing it to normal activities. We would be getting rid of timezones and create something like "activity" zones. It would be a nightmare.
If sunlight had no bearing on human activity, and people didn't tend to follow similar patterns, then utc would be fine.
It appears someone beat me to it, take a look above. It's been a topic of discussion here before, and there are some very good reasons why this is not the case. Like not knowing what time someone might be awake in a different location, or not knowing what business hours might be across the world.