Lots of things would be easier if everybody uses the same time. It could stay the 24h/day time format, but timezones are a pain - I always have to recalculate them for local time. Why couldn't everybody work with UTC? And by the way: when will we finally get rid of the daylight savings time?!?
Consider this. Suppose I want to phone someone who lives in Japan and I live in the UK. Japan is +9 hours ahead of UK local time (GMT). Therefore I know if I phone slightly before lunch then I'll be phoning them in the evening. Now suppose we all had the same time. If I phoned them just before lunch, which would mean shortly before 12:00 in the UK then I'd have to try and figure out what Japan would be doing at that…
So that would need the same exact effort.
The man benefit would be for the "let's meet at the same time online" etc coordination stuff -- where's its brain-dead easy when everybody has the same time.