This seems like it would cause more problems than it solves.
"It's 10:00 here in London. I need to call someone in New York, what time is it there?" "10:00, same as it is everywhere in the world." "So... is now a good time to call them?" "I have no idea."
I'd imagine it would be much easier to remember "business hours in NYC are between 1200 and 2030 UTC," than remembering the time difference and applying a translation every time.
And live shows would only need to advertise events in UTC. DST is almost a symptom of day/night/time discrepancy already but it's a top-down rather than bottom-up approach.
"It's 10:00 here in London. I need to call someone in New York, what time is it there?" "10:00, same as it is everywhere in the world." "So... is now a good time to call them?" "I have no idea."