Time zones tend to come into effect in two situations: when you need to communicate across them, and when you need to travel between them. In the former situation, I agree that having one universal time would simplify things. Also agreed that as long as you tend to stay in one area, it wouldn't be a big deal to get used to dawn at 17:00 or whatever. What I think would be tricky is if you did a lot of traveling. With time zones, you can simply change your watch/phone to local time, then work based on that. With universal time, you would need to either constantly work out what time morning/lunchtime/business hours/etc. are in this new place, or you would have to change your watch/phone to some fictional time to simulate the times you're used to. Either one seems significantly trickier.
Of course, nothing stops people from using UTC only for the situation where it's really useful: long-distance coordination. (And as mentioned in other comments, that's often done already.)
The two situations where time zones are relevant is a very good observation, but I still think we should optimize for the more common case, which is communicating across timezones.
This wouldn't solve much of the communicating across timezones problem - although you may no longer have to look up the canonical time, you instead have to look up the solar time or local time convention (are they sleeping? are they at work?)
So, it's better to keep the second problem ('what time is morning?') more accessible, since you need that in both cases.
The current use of timezones seems primarily designed to ease adjustment for those traveling between them. Work starts at 9 AM in region-X, you move to region-Y, adjust your time and work starts at the "same" time.
Today I think however there are a lot more cases of cross-timezone communications, and a lot of people are telecommuting to work and various events. It may be time to move on and adjust to better support distance communication and telecommuting.
Of course, nothing stops people from using UTC only for the situation where it's really useful: long-distance coordination. (And as mentioned in other comments, that's often done already.)